Worksheets · Pre-Algebra

Histogram worksheet for Pre-Algebra

A histogram groups the data into equal intervals and the bar height is how many landed in each one. Unlike a bar chart the bars touch, because the intervals run on from each other.

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

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Pick more than one for a sheet that mixes them.

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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

    The bar from 20 to 25 holds how many more values than the bar from 30 to 35?10152025303502468101214Frequency
  2. How many of the data values fall below 50?20304050607002468101214Frequency
  3. How many values are in the interval from 25 to 35?202530354045024681012Frequency
  4. Count the values under 20. How many are there?051015202502468101214Frequency
  5. How many of the values lie between 5 and 15?0510152025024681012Frequency

  1. Find a percent from a histogram

    The histogram shows 40 ages of people at a concert, in years, in intervals of 10; each bar includes its left edge but not its right. Find the percent of the 40 people that are 20 or older.1020304050600246810Frequency
  2. A study recorded 20 commute distances, in miles, shown here in bars 5 wide. A bar counts its left edge but not its right. Of the 20 workers, what percent travel less than 20 miles?1015202530350246810Frequency
  3. A histogram sorts 25 race times, in minutes, into intervals 10 wide, each counting its left endpoint and not its right. What percent of the 25 runners took 90 minutes or longer?6070809010011002468Frequency
  4. In the histogram of 25 car speeds on a highway, in miles per hour, every bar is 5 wide and holds its left edge but not its right. What percent of the 25 cars were going slower than 40 miles per hour?3035404550550246810Frequency
  5. Each bar of this histogram of 20 quiz scores, in points, spans 5 units and counts a value on its left edge, not its right. Of the 20 students, what percent scored 30 points or more?2025303540450123456Frequency

  1. Describe the shape of a histogram

    Describe the shape of the histogram, and say whether the mean is greater than, less than or about equal to the median.2030405060700246810Frequency
  2. Skewed left, skewed right or symmetric? Use the shape to compare the mean and the median.4050607080901001100246810Frequency
  3. Is the distribution skewed left, skewed right or symmetric? Is the mean greater than, less than or about equal to the median?203040506070800246810Frequency
  4. Skewed left, skewed right or symmetric? Use the shape to compare the mean and the median.607080901001101201300246810Frequency
  5. Describe the shape of the histogram, and say whether the mean is greater than, less than or about equal to the median.607080901001101200246810Frequency

  1. Find the interval with the median

    The histogram shows 24 whole-number values. Each bar covers ten values and includes its left edge but not its right. In which interval does the median fall?40506070809002468Frequency
  2. 29 sunflowers were measured to the nearest centimeter. Each bar covers ten centimeters and includes its left edge but not its right. Which bar holds the middle value, once the data are put in order?6070809010011002468Frequency
  3. The histogram shows how many pages each of 19 students read this week. Each bar covers ten pages and includes its left edge but not its right. Which interval contains the median?40506070809002468Frequency
  4. The histogram shows the ages of 21 people at a family reunion. Each bar covers ten years and includes its left edge but not its right. Which bar holds the middle value, once the data are put in order?1020304050600123456Frequency
  5. The histogram shows the season point totals of 24 basketball players. Each bar covers ten points and includes its left edge but not its right. In which interval does the median fall?2030405060700246810Frequency

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

Sigma Prep · sigmaprep.io/worksheets

Name

HistogramsAnswer keyVersion 1

Date Period

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

  1. Read a histogram

    The bar from 20 to 25 holds how many more values than the bar from 30 to 35?10152025303502468101214Frequency4
  2. How many of the data values fall below 50?20304050607002468101214Frequency24
  3. How many values are in the interval from 25 to 35?202530354045024681012Frequency13
  4. Count the values under 20. How many are there?051015202502468101214Frequency38
  5. How many of the values lie between 5 and 15?0510152025024681012Frequency16

  1. Find a percent from a histogram

    The histogram shows 40 ages of people at a concert, in years, in intervals of 10; each bar includes its left edge but not its right. Find the percent of the 40 people that are 20 or older.1020304050600246810Frequency80%
  2. A study recorded 20 commute distances, in miles, shown here in bars 5 wide. A bar counts its left edge but not its right. Of the 20 workers, what percent travel less than 20 miles?1015202530350246810Frequency30%
  3. A histogram sorts 25 race times, in minutes, into intervals 10 wide, each counting its left endpoint and not its right. What percent of the 25 runners took 90 minutes or longer?6070809010011002468Frequency36%
  4. In the histogram of 25 car speeds on a highway, in miles per hour, every bar is 5 wide and holds its left edge but not its right. What percent of the 25 cars were going slower than 40 miles per hour?3035404550550246810Frequency20%
  5. Each bar of this histogram of 20 quiz scores, in points, spans 5 units and counts a value on its left edge, not its right. Of the 20 students, what percent scored 30 points or more?2025303540450123456Frequency65%

  1. Describe the shape of a histogram

    Describe the shape of the histogram, and say whether the mean is greater than, less than or about equal to the median.2030405060700246810FrequencySymmetric; the mean and the median are about equal
  2. Skewed left, skewed right or symmetric? Use the shape to compare the mean and the median.4050607080901001100246810FrequencySkewed left; the mean is less than the median
  3. Is the distribution skewed left, skewed right or symmetric? Is the mean greater than, less than or about equal to the median?203040506070800246810FrequencySkewed right; the mean is greater than the median
  4. Skewed left, skewed right or symmetric? Use the shape to compare the mean and the median.607080901001101201300246810FrequencySymmetric; the mean and the median are about equal
  5. Describe the shape of the histogram, and say whether the mean is greater than, less than or about equal to the median.607080901001101200246810FrequencySkewed left; the mean is less than the median

  1. Find the interval with the median

    The histogram shows 24 whole-number values. Each bar covers ten values and includes its left edge but not its right. In which interval does the median fall?40506070809002468Frequency50–59
  2. 29 sunflowers were measured to the nearest centimeter. Each bar covers ten centimeters and includes its left edge but not its right. Which bar holds the middle value, once the data are put in order?6070809010011002468Frequency80–89
  3. The histogram shows how many pages each of 19 students read this week. Each bar covers ten pages and includes its left edge but not its right. Which interval contains the median?40506070809002468Frequency60–69
  4. The histogram shows the ages of 21 people at a family reunion. Each bar covers ten years and includes its left edge but not its right. Which bar holds the middle value, once the data are put in order?1020304050600123456Frequency40–49
  5. The histogram shows the season point totals of 24 basketball players. Each bar covers ten points and includes its left edge but not its right. In which interval does the median fall?2030405060700246810Frequency30–39

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

How to do these

Bars of heights 4,  7 and 2. How many values altogether?

  1. Add the heights.
  2. 4 + 7 + 2.

The answer is 13.

Where students go wrong

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.

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.

Pre-Algebra is usually taken around 7th or 8th 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.