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## Statistics and Probability Worksheets

Welcome to the statistics and probability page at Math-Drills.com where there is a 100% chance of learning something! This page includes Statistics worksheets including collecting and organizing data, measures of central tendency (mean, median, mode and range) and probability.

Students spend their lives collecting, organizing, and analyzing data, so why not teach them a few skills to help them on their way. Data management is probably best done on authentic tasks that will engage students in their own learning. They can collect their own data on topics that interest them. For example, have you ever wondered if everyone shares the same taste in music as you? Perhaps a survey, a couple of graphs and a few analysis sentences will give you an idea.

Statistics has applications in many different fields of study. Budding scientists, stock market brokers, marketing geniuses, and many other pursuits will involve managing data on a daily basis. Teaching students critical thinking skills related to analyzing data they are presented will enable them to make crucial and informed decisions throughout their lives.

Probability is a topic in math that crosses over to several other skills such as decimals, percents, multiplication, division, fractions, etc. Probability worksheets will help students to practice all of these skills with a chance of success!

## Most Popular Statistics and Probability Worksheets this Week

## Mean, Median, Mode and Range Worksheets

Calculating the mean, median, mode and range are staples of the upper elementary math curriculum. Here you will find worksheets for practicing the calculation of mean, median, mode and range. In case you're not familiar with these concepts, here is how to calculate each one. To calculate the mean, add all of the numbers in the set together and divide that sum by the number of numbers in the set. To calculate the median, first arrange the numbers in order, then locate the middle number. In sets where there are an even number of numbers, calculate the mean of the two middle numbers. To calculate the mode, look for numbers that repeat. If there is only one of each number, the set has no mode. If there are doubles of two different numbers and there are more numbers in the set, the set has two modes. If there are triples of three different numbers and there are more numbers in the set, the set has three modes, and so on. The range is calculated by subtracting the least number from the greatest number.

Note that all of the measures of central tendency are included on each page, but you don't need to assign them all if you aren't working on them all. If you're only working on mean, only assign students to calculate the mean.

In order to determine the median, it is necessary to have your numbers sorted. It is also helpful in determining the mode and range. To expedite the process, these first worksheets include the lists of numbers already sorted.

- Calculating Mean, Median, Mode and Range from Sorted Lists Sets of 5 Numbers from 1 to 10 Sets of 5 Numbers from 10 to 99 Sets of 5 Numbers from 100 to 999 Sets of 10 Numbers from 1 to 10 Sets of 10 Numbers from 10 to 99 Sets of 10 Numbers from 100 to 999 Sets of 20 Numbers from 10 to 99 Sets of 15 Numbers from 100 to 999

Normally, data does not come in a sorted list, so these worksheets are a little more realistic. To find some of the statistics, it will be easier for students to put the numbers in order first.

- Calculating Mean, Median, Mode and Range from Unsorted Lists Sets of 5 Numbers from 1 to 10 Sets of 5 Numbers from 10 to 99 Sets of 5 Numbers from 100 to 999 Sets of 10 Numbers from 1 to 10 Sets of 10 Numbers from 10 to 99 Sets of 10 Numbers from 100 to 999 Sets of 20 Numbers from 10 to 99 Sets of 15 Numbers from 100 to 999

## Collecting and Organizing Data

Teaching students how to collect and organize data enables them to develop skills that will enable them to study topics in statistics with more confidence and deeper understanding.

- Constructing Line Plots from Small Data Sets Construct Line Plots with Smaller Numbers and Lines with Ticks Provided (Small Data Set) Construct Line Plots with Smaller Numbers and Lines Only Provided (Small Data Set) Construct Line Plots with Smaller Numbers (Small Data Set) Construct Line Plots with Larger Numbers and Lines with Ticks Provided (Small Data Set) Construct Line Plots with Larger Numbers and Lines Only Provided (Small Data Set) Construct Line Plots with Larger Numbers (Small Data Set)
- Constructing Line Plots from Larger Data Sets Construct Line Plots with Smaller Numbers and Lines with Ticks Provided Construct Line Plots with Smaller Numbers and Lines Only Provided Construct Line Plots with Smaller Numbers Construct Line Plots with Larger Numbers and Lines with Ticks Provided Construct Line Plots with Larger Numbers and Lines Only Provided Construct Line Plots with Larger Numbers

## Interpreting and Analyzing Data

Answering questions about graphs and other data helps students build critical thinking skills. Standard questions include determining the minimum, maximum, range, count, median, mode, and mean.

- Answering Questions About Stem-and-Leaf Plots Stem-and-Leaf Plots with about 25 data points Stem-and-Leaf Plots with about 50 data points Stem-and-Leaf Plots with about 100 data points
- Answering Questions About Line Plots Line Plots with Smaller Data Sets and Smaller Numbers Line Plots with Smaller Data Sets and Larger Numbers Line Plots with Larger Data Sets and Smaller Numbers Line Plots with Larger Data Sets and Larger Numbers
- Answering Questions About Broken-Line Graphs Answer Questions About Broken-Line Graphs
- Answering Questions About Circle Graphs Circle Graph Questions (Color Version) Circle Graph Questions (Black and White Version) Circle Graphs No Questions (Color Version) Circle Graphs No Questions (Black and White Version)
- Answering Questions About Pictographs Answer Questions About Pictographs

## Probability Worksheets

- Calculating Probabilities with Dice Sum of Two Dice Probabilities Sum of Two Dice Probabilities (with table)

Spinners can be used for probability experiments or for theoretical probability. Students should intuitively know that a number that is more common on a spinner will come up more often. Spinning 100 or more times and tallying the results should get them close to the theoretical probability. The more sections there are, the more spins will be needed.

- Calculating Probabilities with Number Spinners Number Spinner Probability (4 Sections) Number Spinner Probability (5 Sections) Number Spinner Probability (6 Sections) Number Spinner Probability (7 Sections) Number Spinner Probability (8 Sections) Number Spinner Probability (9 Sections) Number Spinner Probability (10 Sections) Number Spinner Probability (11 Sections) Number Spinner Probability (12 Sections)

Non-numerical spinners can be used for experimental or theoretical probability. There are basic questions on every version with a couple extra questions on the A and B versions. Teachers and students can make up other questions to ask and conduct experiments or calculate the theoretical probability. Print copies for everyone or display on an interactive white board.

- Probability with Single-Event Spinners Animal Spinner Probability ( 4 Sections) Animal Spinner Probability ( 5 Sections) Animal Spinner Probability ( 10 Sections) Letter Spinner Probability ( 4 Sections) Letter Spinner Probability ( 5 Sections) Letter Spinner Probability ( 10 Sections) Color Spinner Probability ( 4 Sections) Color Spinner Probability ( 5 Sections) Color Spinner Probability ( 10 Sections)
- Probability with Multi-Event Spinners Animal/Letter Combined Spinner Probability ( 4 Sections) Animal/Letter Combined Spinner Probability ( 5 Sections) Animal/Letter Combined Spinner Probability ( 10 Sections) Animal/Letter/Color Combined Spinner Probability ( 4 Sections) Animal/Letter/Color Combined Spinner Probability ( 5 Sections) Animal/Letter/Color Combined Spinner Probability ( 10 Sections)

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## Statistics Worksheets Hub Page

Welcome to our Statistics Worksheets hub page.

Here you will find links to lots of data handling and analysis worksheet webpages, which will help your child become more confident in handling and interpreting a range of data.

Why not take a look at some of our bar graph worksheets, or have a go at some of our Mean, Median and Mode sheets?

We also have a selection of venn diagram and line graph worksheets.

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- This page contains links to other Math webpages where you will find a range of activities and resources.
- If you can't find what you are looking for, try searching the site using the Google search box at the top of each page.

## Geometry Worksheets

Resources by Grade

## 1st Grade Statistics

2nd grade statistics, 3rd grade statistics, 4th grade statistics, 5th grade statistics, 6th grade statistics.

Resources by Topic

- Tally Charts
- Line Graphs
- Mode, Median, Mean and Range
- Box Plots & Dot Plots

## Resources Indexed by Grade

- Tally Chart Worksheets
- Bar Graphs First Grade
- Line Plots 2nd Grade
- Bar Graphs 2nd Grade
- Venn Diagram Worksheets 2nd Grade
- Line Plot Worksheets 3rd grade
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- 3 Circle Venn Diagram Worksheets
- Median Worksheets
- Mean Worksheets
- Mode and Range Worksheets
- Mean Median Mode and Range Worksheets
- Box Plot Worksheets

Here is our selection of tally chart worksheets for 1st and 2nd graders.

These sheets involve counting and recording tallies.

## Line Plot Worksheets

These worksheets involve creating and interpreting a range of line plots.

Here you will find our range of statistics worksheets involving using bar graphs, picture graphs and line graphs.

There is a wide range of different sheets at each level, and each sheet comes with its own set of answers.

## Line Graph Worksheets

Here is our selection of line graph worksheets.

The worksheets on this page involve plotting and analysing a range of line graphs.

Using these sheets will help your child to:

- plot points on a line graph;
- analyse data points on a line graph;
- answer questions involving line graphs.

## Venn Diagram Worksheets

Here are our selection of venn diagram worksheets to help you sort a range of different objects.

There are a selection of 2 and 3 circle venn diagram worksheets.

Our worksheets cover sorting animals and people, to sorting shapes and numbers.

- What is a venn diagram page

## Mode, Mean, Median and Range

Find links to our Median worksheets below.

Using this webapge will help you to:

- find the median of a set of data;
- find the median of both odd and even numbers of data points;
- show you worked examples of how to find the median.

Find links to our Mean worksheets below.

Using these sheets will help you to:

- find the mean of up to 5 numbers;
- find the mean of a range of numbers, including negative numbers and decimals;
- find a missing data point when the mean is given.

Find links to our Mode and Range worksheets below.

- find the mode of a list of numbers numbers;
- find the range of a list of numbers;
- see worked examples of how to find the mode and range of a set of data.

The sheets in this section will help you to find the mean, median, mode and range of a set of numbers, including negative numbers and decimals.

There are easier sheets involving fewer data points, and harder ones with more data points.

- Lower Quartile and Upper Quartile Support Page

## Box Plot & Dot Plots

Here are our selection of box plot worksheets to help you practice creating and interpreting box plots.

- What is a Box Plot?
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These worksheets will help you to create and interpret a range of dot plots.

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## Generating PDF...

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## Most Used Actions

Number line.

- arithmetic\:mean\:1,\:2,\:3,\:4,\:5,\:6
- geometric\:mean\:\left\{0.42,\:0.52,\:0.58,\:0.62\right\}
- quadratic\:mean\:-4,\:5,\:6,\:9
- median\:\:\left\{1,\:7,\:-3,\:4,\:9\right\}
- mode\:\left\{90,\:94,\:53,\:68,\:79,\:94,\:87,\:90,\:70,\:69,\:65,\:89,\:85\right\}
- minimum\:-4,\:5,\:6,\:9
- maximum\:\frac{31}{100},\:\frac{23}{105},\:\frac{31}{205},\:\frac{54}{205}
- mid\:range\:1,\:2,\:3,\:4,\:5,\:6
- range\:\:\left\{1,\:7,\:-3,\:4,\:9\right\}
- standard\:deviation\:\:\left\{1,\:7,\:-3,\:4,\:9\right\}
- variance\:1,\:2,\:3,\:4,\:5,\:6
- lower\:quartile\:-4,\:5,\:6,\:9
- upper\:quartile\:\left\{0.42,\:0.52,\:0.58,\:0.62\right\}
- interquartile\:range\:1,\:2,\:3,\:4,\:5,\:6
- midhinge\:\left\{90,\:94,\:53,\:68,\:79,\:84,\:87,\:72,\:70,\:69,\:65,\:89,\:85\right\}
- What is the best calculator for statistics?
- Symbolab offers an online calculator specifically for statistics that can perform a wide range of calculations, including standard deviation, variance, range and normal distribution. It also provides detailed step-by-step solutions.
- What is statistics?
- Statistics is the branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. There are two main branches of statistics: descriptive statistics, and inferential statistics.
- What is descriptive statistics?
- Descriptive statistics is a branch of statistics that deals with summarizing, organizing and describing data. Descriptive statistics uses measures such as central tendency (mean, median, and mode) and measures of variability (range, standard deviation, variance) to give an overview of the data.
- What is inferential statistics?
- Inferential statistics is a branch of statistics that deals with making predictions and inferences about a population based on a sample of data. Inferential statistics uses probability theory and statistical models to make predictions and inferences about a population.
- What is the difference between statistics and probability?
- Statistics is the branch of mathematics dealing with the collection, analysis, interpretation, presentation, and organization of data, while probability is the branch of mathematics dealing with the likelihood of occurrence of different events.

statistics-calculator

- Lies, Damned Lies, and Statistics Statistics is about analyzing data, for instance the mean is commonly used to measure the “central tendency” of... Read More

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Work in groups on these problems. You should try to answer the questions without referring to your textbook. If you get stuck, try asking another group for help.

## Student Learning Outcomes

- The student will compare and contrast empirical data from a random number generator with the uniform distribution.

## Collect the Data

Use a random number generator to generate 50 values between zero and one (inclusive). List them in Table . Round the numbers to four decimal places or set the calculator MODE to four places.

- \(\bar{x}\)= _______
- s = _______
- first quartile = _______
- third quartile = _______
- median = _______

## Organize the Data

## Describe the Data

- In two to three complete sentences, describe the shape of each graph. (Keep it simple. Does the graph go straight across, does it have a V shape, does it have a hump in the middle or at either end, and so on. One way to help you determine a shape is to draw a smooth curve roughly through the top of the bars.)
- Describe how changing the number of bars might change the shape.

## Theoretical Distribution

- In words, \(X\) = _____________________________________.
- The theoretical distribution of \(X\) is \(X\) ~ U (0,1).
- \(\mu\) = ______
- \(\sigma\) = ______
- first quartile = ______
- third quartile = ______
- median = __________
- Are the empirical values (the data) in the section titled Collect the Data close to the corresponding theoretical values? Why or why not?

## Plot the Data

- Construct a box plot of the data. Be sure to use a ruler to scale accurately and draw straight edges.
- Do you notice any potential outliers? If so, which values are they? Either way, justify your answer numerically. (Recall that any DATA that are less than Q 1 – 1.5( IQR ) or more than Q 3 + 1.5( IQR ) are potential outliers. IQR means interquartile range.)

## Compare the Data

- minimum value: _______
- first quartile: _______
- median: _______
- third quartile: _______
- maximum value: _______
- width of IQR : _______
- overall shape: _______
- Based on your comments in the section titled Collect the Data , how does the box plot fit or not fit what you would expect of the distribution in the section titled Theoretical Distribution ?

## Discussion Question

- Suppose that the number of values generated was 500, not 50. How would that affect what you would expect the empirical data to be and the shape of its graph to look like?

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## Random Sampling

Here we will learn about random sampling, including what random sampling is, how to take a random sample of data, and the advantages and disadvantages of this sampling method.

There are also random sampling worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.

## What is random sampling?

Random sampling is a type of sampling method.

To take a random sample, we list each individual member of the population, assign a unique number to each member, and use a random number generator or a random number table to select the number of pieces of data required for the sample size.

We use simple random sampling to choose the individual items of data within the population .

Each member of the sample has an equal chance of being selected, reducing bias and sampling error .

Random sampling is also used for other sampling techniques such as stratified sampling.

Stratified sampling requires another sampling method such as a simple random sample to generate a random selection of data values once the data is divided into subgroups (or subsets ). This means that each item of data has an equal probability of being chosen and each subgroup within the sample is represented proportionally to the whole population.

Other types of random sampling methods include: cluster sampling, stratified sampling , and systematic sampling .

There are also other types of sampling methods that do not require simple random sampling include: quota sampling , convenience sampling ( non-random sampling ), non-probability sampling , and snowball sampling .

## Advantages and disadvantages of random sampling

Following a random sampling methodology has advantages and disadvantages:

## Sampling error

If every member of the population is in the sample, there is no sampling error. As the sample gets smaller, or the methodology has introduced a selection bias , the sampling error becomes more significant as this means that the sample may not be representative of the population.

The more random a sample is, the smaller the sampling error .

## What happens next?

Once a random sample is chosen, the next step is data collection where respondents offer data to fulfill the requirements of the questionnaire or survey (for example). The collected values within the sample then go through data analysis to find generalised results for the population.

## How to take a random sample

In order to take a random sample:

List every member of the population.

Associate each member of the population with a unique reference number.

Use a random number generator to select the number of data points in the sample.

## Types of sampling methods worksheet (includes random sampling)

Get your free random sampling worksheet of 20+ types of sampling methods questions and answers. Includes reasoning and applied questions.

## Related lessons on types of sampling methods

Random sampling is part of our series of lessons to support revision on types of sampling methods . You may find it helpful to start with the main types of sampling methods lesson for a summary of what to expect, or use the step by step guides below for further detail on individual topics. Other lessons in this series include:

- Types of sampling methods
- Capture recapture
- Stratified sampling
- Systematic sampling
- Collecting data

## Random sampling examples

Example 1: deck of cards.

A deck of cards contains 52 cards divided into 4 suits. Use a random number generator to collect a sample of 5 cards from one suit. Do not allow any duplicates.

The 13 cards in one suit are: Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King.

2 Associate each member of the population with a unique reference number.

3 Use a random number generator to select the number of data points in the sample.

Using a Casio FX series calculator, we can generate random numbers between 1 and 13 by pressing the key combination:

1, 3, × , shift, . , =

This should show the expression: 13 × RAN # =. Round any decimal to the nearest integer (whole number). Ignore any duplicates as stated in the question.

The 5 cards in the sample are: Ace, 5, 6, 7, Jack.

## Example 2: the alphabet

There are 26 letters in the English alphabet. Use a random sample to obtain a sample of 10 letters with no duplicates.

Here we will list all 26 letters of the English alphabet.

A = 1, B=2, etc:

Using a Casio FX series calculator, we can generate random numbers between 1 and 26 by pressing the key combination:

2, 6, ×, shift, . , =

This should show the expression: 26 × RAN #=. Round any decimal to the nearest integer (whole number). Ignore any duplicates as stated in the question.

The 10 letters in the sample are: F, W, E, P, L, M, A, Y, N, J.

## Example 3: questionnaire

A class of 20 students completed a questionnaire. Of the 20 students a random sample of 30% will be given a prize. Each student is given a number between 1 and 20 determined by their position in the register. Determine which students will be given a prize. Each student can only receive one prize.

As each student has been given a number between 1 and 20 , we do not need to know their names in order to choose the sample. We therefore only need to reference the numbers between 1 and 20 .

As each member of the population is numbered between 1 and 20 , we can use this number.

Using a Casio FX series calculator, we can generate random numbers between 1 and 20 by pressing the key combination:

2, 0, ×, shift, . , =

This should show the expression: 20 × RAN #=. Round any decimal to the nearest integer (whole number). Ignore any duplicates as stated in the question.

As we need to obtain 30% of the students, we need to calculate 30% of 20

20\div{100}\times{30}=6\text{ students} .

The 6 students in the sample who win a prize are: 2, 3, 5, 7, 9, and 19 .

## Example 4: counters

There are 36 counters in a bag. Each counter is uniquely numbered with a two digit number that can be determined by rolling two fair, six sided dice. Counters are chosen by the number rolled on the first dice being the first digit, and the number rolled on the second dice being the second digit. A sample of 12 counters is chosen from the bag. Each counter is replaced and so can be chosen twice. Determine the numbers on the 12 counters.

As each dice has the numbers 1 to 6 , we have the following sample space:

Each member of the population (each counter) has a unique reference number

This time, as each dice is fair, we can use the dice to generate the 12 counters from the bag. Rolling the dice together 12 times, and allowing repetitions, we obtain the following random sample:

## Example 5: student survey

A school wants to investigate what students in the new Year 7 cohort eat for lunch. The school is expecting 250 new students in Year 7 . They wish to take a sample of 10% of the students. Each student is ordered alphabetically by their surname and given a unique number between 1 and 250 . Use a random number generator to determine the students who will participate in the investigation.

As there are 250 students in the population, we would use a list to determine each unique reference number. For this example, we will visualise the list without writing down all 250 numbers!

Each member of the population has a unique reference number as stated in the question and so we can move on to step 3 .

As we need a sample of 10% , we need to obtain a sample of 25 students as 10% of 250 is equal to 25 .

Using a Casio FX series calculator, we can generate random numbers between 1 and 250 by pressing the key combination:

2, 5, 0, ×, shift, . , =

This should show the expression: 250 × RAN #=. Round any decimal to the nearest integer (whole number). Ignore any duplicates as stated in the question.

The students involved in the investigation are:

## Example 6: production line

A production line produces 1000 tubes of toothpaste every hour. In one 8 hour day, 0.1% of the tubes must be taken off of the production line for quality control testing. These tubes must be chosen at random to ensure that the product quality remains consistent throughout production. Determine the tubes that are selected for quality control in one day. Do not include duplicated data.

As there are 1000 tubes per hour and 8 hours in one day, there are 8000 potential items of data. Theoretically we could list all 8000 items but this would be unnecessary and very time consuming.

Each tube is numbered from 1-8000 depending on their place in the production line (chronologically).

As we need a sample of 0.1% , we need to calculate 0.1% of 8000 :

(8000\div{100})\times{0.1}=8\text{ tubes} .

Using a Casio FX series calculator, we can generate random numbers between 1 and 250 by pressing the key combination:

1000, ×, shift, . , =

This should show the expression: 1000 × RAN #=. Each number will be an integer and so we can use this number to select the item in the population for the sample.

The tubes taken off of the production line for quality control testing are numbers: 275, 278, 383, 394, 662, 801, 908, and 979.

## Common misconceptions

- Mixing up a sampling method

Using the incorrect sampling method to select data (such as using systematic sampling or non random sampling)

- Using the RAN# button incorrectly

The RAN# button returns a number to 3 decimal places. Different calculators will have different ways to generate random numbers over an interval and so make sure you know how your calculator does this function.

- Incorrect number of items in the sample / duplicates

If a sample asks for a specific number of data values, then the sample must contain this number of data. Be careful as to whether the sample can contain duplicates as some will allow repeated results.

## Practice random sampling questions

1. 1000 people enter a running race. Each person is given a race number to attach to his/her shirt to track their position in the race. At the end of the race, 10 runners are randomly selected for a drug test. Describe how they should be selected using a simple random sampling method.

Take the first 10 people to cross the finish line.

Select the first runner at random then take every 100^\text{th} person who crosses the line.

Use a random number generator to select 10 random numbers between 1 and 1000 .

Use a random number generator to select the order of all 1000 runners in the population.

As each runner has a unique race number, these numbers can be placed into a random number generator to minimise the bias when selecting runners for the drug test. This would be a suitable way to select a simple random sample.

2. An article in a newspaper contains 1500 words. The editor would like to find out the reading age of the article by taking a random sample of words and calculating the average word length. The location of each word in the article is numbered from 1-1500 Describe how you would take a random sample of 25% of the words in the article.

Use the first 375 words in the article.

Find the average word length of all 1500 words.

Select the first word out of the first 4 words at random, then use every fourth word in the article following this.

Use a random number generator to select 375 random numbers between 1 and 1500 .

For a random sample of 25 % of the words in the article, we need to calculate 25 % of the population. Here, 25 % of 1500 is 375 words.

As the location of each word is numbered (e.g. the first word in this paragraph “For” would be labelled 1 , “a” would be labelled 2, etc.) we can use a random number generator to select 375 numbers out of a possible 1500 , and therefore select the 375 words for the sample.

3. There are nearly 300 weather stations across a county. A sample of 15 weather stations are routinely checked every year to ensure the equipment is working optimally. Each weather station is named alphabetically by the road/street name it is located by. Describe how you would take a random sample of 15 weather stations.

Assign each weather station a random number then use a random number generator to select 15 weather stations.

Divide the list into smaller groups according to their height, find the proportion within each subgroup for the sample then select the tallest weather stations in each group.

Select the last 15 weather stations that appear in the list alphabetically.

Check every weather station in the county.

As the 300 weather stations can be listed in alphabetical order, we can assign each weather station with a unique reference number. Using a random number generator to select 15 numbers out of the list of 300 would successfully select 15 weather stations. This would be a random sample.

4. An astronomer is exploring the night sky using a telescope. He wants to count the number of shooting stars in the sky over a 12 hour period. He decides to observe for 15 minute intervals chosen randomly throughout the night. He wants to observe for at least 6 hours. Describe how he should choose a random sample of data.

Observe for 15 minutes every half an hour throughout the night.

Observe for the entire night

Assign each interval a consecutive number between 1 and 48 . Use a random number generator to select 24 intervals. No duplicates.

Assign each interval a consecutive number between 1 and 48 . Use a random number generator to select 6 intervals over the 12 hours. No duplicates.

There are four, 15 minute intervals each hour. Over 6 hours, this would be 24 intervals ( 6 4=24 ). A 12 hour period would have a total of 48 intervals ( 12 4=48 ). Labelling each subsequent interval with a unique reference number, we can put the 48 intervals into a random number generator to select the 24 intervals needed for the sample. This would generate a random sample for the research.

5. A deck of cards is shuffled and placed face down on a table so that you cannot see what is on each card. Describe how you would use a random sampling method to pick 13 cards.

Split the deck in half and take the next 13 cards from the top of the pile.

Turn all of the cards over and pick all of the Spades out of the deck.

Pick every fourth card from the pile.

Assign the top card as number 1 through to number 52 . Use a random number generator to choose 13 random numbers between 1 and 52 .

As the deck of cards is face down, each card can be numbered from 1 to 52 (the top card in the deck would be number 1 , the bottom card in the deck would be number 52 etc). As each card has a unique reference number, we can use a random number generator to select the 13 cards in the sample. This would mean that each card has an equal chance of being selected for the sample.

6. A CCTV camera captures the number of people crossing a busy junction 24 hours a day. A road safety company would like to determine whether a pedestrian crossing should be installed in the area. They decide to take a random sample of hours throughout one week to monitor how many pedestrians cross the junction. Determine how they should take a random sample of times.

Associate each hour with a unique reference number and use a random number generator to determine which hours will be used in the sample.

Observe the CCTV camera continuously for the entire week, recording the total number of pedestrians that cross the junction.

Record the number of pedestrians that cross the junction between 7-9 am, and 4-6 pm Monday to Friday.

Divide the number of hours per day by the number of letters in each day (M-O-N-D-A-Y = 6 ) to determine how many hours of CCTV is recorded overnight.

There are 168 hours in one week. If we assign each hour a unique reference number (hour 1 is Monday 00:00 , hour 2 is Monday 01:00 etc), then we would place 168 numbers into a random number generator, in order for that generator to select the sample size. This would be a random sample as there are no subgroups for the sample to be stratified, and the numbers are not selected using a sequence (a systematic sample).

## Random sampling GCSE questions

1. Freddie is investigating the distribution of prime numbers. He knows that there are 25 prime numbers between 1 and 100 . He uses a random number generator to select 20 numbers between 1 and 100 . Below are his results:

Freddie states “These numbers are not random”.

(a) Why would Freddie think that these numbers are not random?

(b) How could this investigation be improved?

Only 2/20 are prime numbers

He should expect 5 numbers to be prime as 25% of 20 is 5

There are lots of patterns (numbers ending in a 4 or 5 )

Take a larger sample

2. (a) There are 26 letters in the English Alphabet. Use a random sampling method to obtain a sample of 5 letters with no duplicates. Use the grid below to help you.

(b) Harriet says her sample consists of the letters “PQRST” . Do you think these letters were chosen at random? Explain your answer.

Each letter associated with a unique reference number

5 random numbers / letters selected with no obvious pattern / order

Unlikely they are chosen at random (not impossible)

They are all consecutive letters

3. Two dice are rolled 1000 times and their scores are added together. Roger wants to check the validity of the experiment and so he takes a sample of 2% of the data. Below are the values in the sample.

Should the results of the experiment be trusted? Explain your answer.

4/20 items of data are not possible solutions for the sum of two dice

( 1, 0, 13, 1 not possible for the sum of two dice)

## Learning checklist

You have now learned how to:

- Infer properties of populations or distributions from a sample, whilst knowing the limitations of sampling

## The next lessons are

- Types of data
- Frequency table
- Mean, median, mode

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## 1.1.22: Sampling Experiment (Worksheet)

- Last updated
- Save as PDF
- Page ID 1337

Name: ______________________________

Section: _____________________________

Student ID#:__________________________

Work in groups on these problems. You should try to answer the questions without referring to your textbook. If you get stuck, try asking another group for help.

## Student Learning Outcomes

- The student will demonstrate the simple random, systematic, stratified, and cluster sampling techniques.
- The student will explain the details of each procedure used.

In this lab, you will be asked to pick several random samples of restaurants. In each case, describe your procedure briefly, including how you might have used the random number generator, and then list the restaurants in the sample you obtained.

The following section contains restaurants stratified by city into columns and grouped horizontally by entree cost (clusters).

Restaurants Stratified by City and Entree Cost

A Simple Random Sample

Pick a simple random sample of 15 restaurants.

- Describe your procedure.

A Systematic Sample

Pick a systematic sample of 15 restaurants.

A Stratified Sample

Pick a stratified sample , by city, of 20 restaurants. Use 25% of the restaurants from each stratum. Round to the nearest whole number.

Pick a stratified sample , by entree cost, of 21 restaurants. Use 25% of the restaurants from each stratum. Round to the nearest whole number.

A Cluster Sample

Pick a cluster sample of restaurants from two cities. The number of restaurants will vary.

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Descriptive Statistics in Excel. By Jim Frost 38 Comments. Descriptive statistics summarize your dataset, painting a picture of its properties. These properties include various central tendency and variability measures, distribution properties, outlier detection, and other information. Unlike inferential statistics, descriptive statistics only ...

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Describe how you would use a random sampling method to pick 13 13 cards. Split the deck in half and take the next 13 13 cards from the top of the pile. Turn all of the cards over and pick all of the Spades out of the deck. Pick every fourth card from the pile. Assign the top card as number 1 1 through to number 52 52.

This page titled 1.1.22: Sampling Experiment (Worksheet) is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by OpenStax via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request. The student will demonstrate the simple random, systematic ...