Worksheets · Statistics

Histogram worksheet for Statistics

Statistics reads a histogram for shape, center and spread: a long tail pulls the mean toward it, so a right-skewed set has its mean above its median. You also find the interval that holds the median, the percent of values past a cutoff, and the total count.

Also taught in Pre-Algebra and Algebra 1, each at its own level and with its own examples.

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Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Histograms

Date Period

Use the histogram to answer each question. Each bar includes its left edge but not its right.

  1. Read a histogram

    Find how many more values lie from 15 to 20 than from 5 to 10.0510152025024681012Frequency
  2. Count the values under 50. How many are there?10203040506002468101214Frequency
  3. How many of the values lie between 50 and 70?20304050607002468101214Frequency
  4. The bar from 20 to 25 holds how many more values than the bar from 30 to 35?20253035404502468101214Frequency
  5. Find the number of data values from 10 up to 30.10203040506002468101214Frequency

  1. Find a percent from a histogram

    A histogram sorts 25 daily high temperatures, in degrees Fahrenheit, into intervals 10 wide, each counting its left endpoint and not its right. Find the percent of the 25 days that reached 70 degrees or more.50607080901000246810Frequency
  2. The histogram groups 20 reading times last week, in minutes, into bars 5 wide. A value on the edge between two bars counts in the bar to its right. Of the 20 students, what percent read for less than 35 minutes?2530354045500123456Frequency
  3. A study recorded 20 car speeds on a highway, in miles per hour, shown here in bars 10 wide. A bar counts its left edge but not its right. What percent of the 20 cars were going slower than 80 miles per hour?6070809010011002468Frequency
  4. In the histogram of 25 commute distances, in miles, every bar is 5 wide and holds its left edge but not its right. What percent of the 25 workers travel less than 25 miles?1015202530350246810Frequency
  5. Each bar of this histogram of 20 package weights, in pounds, spans 10 units and counts a value on its left edge, not its right. Find the percent of the 20 packages that weigh 20 pounds or more.10203040506002468Frequency

  1. Describe the shape of a histogram

    Skewed left, skewed right or symmetric? Use the shape to compare the mean and the median.50607080901001100246810Frequency
  2. Is the distribution skewed left, skewed right or symmetric? Is the mean greater than, less than or about equal to the median?3040506070800246810Frequency
  3. Describe the shape of the histogram, and say whether the mean is greater than, less than or about equal to the median.304050607080901000246810Frequency
  4. Skewed left, skewed right or symmetric? Use the shape to compare the mean and the median.40506070809010002468Frequency
  5. Is the distribution skewed left, skewed right or symmetric? Is the mean greater than, less than or about equal to the median?40506070809002468Frequency

  1. Find the interval with the median

    23 students timed their bike ride to school, in whole minutes. Each bar covers ten minutes and includes its left edge but not its right. Which interval contains the median?607080901001100246810Frequency
  2. 24 students took a test, and their scores are graphed below. Each bar covers ten scores and includes its left edge but not its right. Which bar holds the two middle values, once the data are put in order?3040506070800246810Frequency
  3. 30 guests at a wedding gave their ages, graphed in the histogram. Each bar covers ten years and includes its left edge but not its right. In which interval does the median fall?2030405060700246810Frequency
  4. The histogram shows the heights of 25 tomato plants, in whole centimeters. Each bar covers ten centimeters and includes its left edge but not its right. In which interval does the median fall?607080901001100246810Frequency
  5. 23 players each kept a season total of points, graphed below. Each bar covers ten points and includes its left edge but not its right. Which bar holds the middle value, once the data are put in order?506070809010002468Frequency

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

HistogramsAnswer keyVersion 3

Date Period

Use the histogram to answer each question. Each bar includes its left edge but not its right.

  1. Read a histogram

    Find how many more values lie from 15 to 20 than from 5 to 10.0510152025024681012Frequency6
  2. Count the values under 50. How many are there?10203040506002468101214Frequency33
  3. How many of the values lie between 50 and 70?20304050607002468101214Frequency20
  4. The bar from 20 to 25 holds how many more values than the bar from 30 to 35?20253035404502468101214Frequency4
  5. Find the number of data values from 10 up to 30.10203040506002468101214Frequency18

  1. Find a percent from a histogram

    A histogram sorts 25 daily high temperatures, in degrees Fahrenheit, into intervals 10 wide, each counting its left endpoint and not its right. Find the percent of the 25 days that reached 70 degrees or more.50607080901000246810Frequency80%
  2. The histogram groups 20 reading times last week, in minutes, into bars 5 wide. A value on the edge between two bars counts in the bar to its right. Of the 20 students, what percent read for less than 35 minutes?2530354045500123456Frequency40%
  3. A study recorded 20 car speeds on a highway, in miles per hour, shown here in bars 10 wide. A bar counts its left edge but not its right. What percent of the 20 cars were going slower than 80 miles per hour?6070809010011002468Frequency50%
  4. In the histogram of 25 commute distances, in miles, every bar is 5 wide and holds its left edge but not its right. What percent of the 25 workers travel less than 25 miles?1015202530350246810Frequency44%
  5. Each bar of this histogram of 20 package weights, in pounds, spans 10 units and counts a value on its left edge, not its right. Find the percent of the 20 packages that weigh 20 pounds or more.10203040506002468Frequency85%

  1. Describe the shape of a histogram

    Skewed left, skewed right or symmetric? Use the shape to compare the mean and the median.50607080901001100246810FrequencySymmetric; the mean and the median are about equal
  2. Is the distribution skewed left, skewed right or symmetric? Is the mean greater than, less than or about equal to the median?3040506070800246810FrequencySkewed left; the mean is less than the median
  3. Describe the shape of the histogram, and say whether the mean is greater than, less than or about equal to the median.304050607080901000246810FrequencySymmetric; the mean and the median are about equal
  4. Skewed left, skewed right or symmetric? Use the shape to compare the mean and the median.40506070809010002468FrequencySkewed right; the mean is greater than the median
  5. Is the distribution skewed left, skewed right or symmetric? Is the mean greater than, less than or about equal to the median?40506070809002468FrequencySkewed right; the mean is greater than the median

  1. Find the interval with the median

    23 students timed their bike ride to school, in whole minutes. Each bar covers ten minutes and includes its left edge but not its right. Which interval contains the median?607080901001100246810Frequency70–79
  2. 24 students took a test, and their scores are graphed below. Each bar covers ten scores and includes its left edge but not its right. Which bar holds the two middle values, once the data are put in order?3040506070800246810Frequency50–59
  3. 30 guests at a wedding gave their ages, graphed in the histogram. Each bar covers ten years and includes its left edge but not its right. In which interval does the median fall?2030405060700246810Frequency40–49
  4. The histogram shows the heights of 25 tomato plants, in whole centimeters. Each bar covers ten centimeters and includes its left edge but not its right. In which interval does the median fall?607080901001100246810Frequency90–99
  5. 23 players each kept a season total of points, graphed below. Each bar covers ten points and includes its left edge but not its right. Which bar holds the middle value, once the data are put in order?506070809010002468Frequency80–89

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

How to do these

Bars: 0–9 (2), 10–19 (5), 20–29 (8), 30–39 (4), 40–49 (1). Which interval holds the median?

  1. There are 20 values, so the median is between the 10th and 11th.
  2. Running totals: 2, then 7, then 15.
  3. Both the 10th and 11th values fall in the third bar.

The answer is 20–29.

Where students go wrong

Naming the skew for the side where the bars are tall. Skewed right means the long tail stretches to the right, so the tall bars are on the left.

Also called reading a histogram or bar graph intervals.

What you can put on this worksheet

Reading a histogram
Name the lower bound of the interval that holds the most values. — a histogram of 4 intervals starting at 10 → 10
Make a histogram from data
Draw a histogram of the numbers of visitors to a museum each day. Start the first bar at 20 and make each bar 10 wide. A value on the edge between two bars goes in the bar to its right: 40 belongs in the bar from 40 to 50. Data: 41, 33, 27, 42, 34, 45, 44, 40, 33, 38, 35, 48, 33, 51, 40. → 20–29: 1, 30–39: 6, 40–49: 7, 50–59: 1
Percent above or below a cutoff
The histogram groups 25 homework times, in minutes, into bars 5 wide. A value on the edge between two bars counts in the bar to its right. Of the 25 students, what percent spent less than 20 minutes? → 68%
The shape, and mean against median
Describe the shape of this histogram: skewed left, skewed right or symmetric. — a histogram of 7 intervals starting at 10 → Skewed left
Which interval holds the median
The histogram shows how many minutes each of 19 runners took to finish a race, in whole minutes. Each bar covers ten minutes and includes its left edge but not its right. Which bar holds the middle value, once the data are put in order? → 40–49
Choose your own intervals
Sort these values into equal-width intervals and show the counts as a histogram: 67, 76, 43, 64, 68, 52, 88, 56, 82, 67, 88, 44, 71, 60. → One answer:
40–49: 2, 50–59: 2, 60–69: 5, 70–79: 2, 80–89: 3

Questions about these worksheets

Yes. Every histogram sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Statistics is usually taken around 11th or 12th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the histogram questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

You pick from 6: reading a histogram, make a histogram from data, percent above or below a cutoff, the shape, and mean against median, which interval holds the median and choose your own intervals. Tick as many as you want and set how many of each, or let it spread them evenly.

Answering with the bar height when the question asked for the interval, or the other way round. Height is the count, the label underneath is the value.