Worksheets · Algebra 1

Histogram worksheet for Algebra 1

Algebra 1 uses histograms to describe a data set by its shape, skewed left, skewed right or symmetric, and to say what that shape means for the mean against the median. Questions also ask for totals, the percent of values past a cutoff, and which interval holds the median.

Also taught in Pre-Algebra 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

    Count the values under 30. How many are there?20253035404502468101214Frequency
  2. How many of the values lie between 10 and 30?01020304050024681012Frequency
  3. How many more values are in the interval from 50 to 60 than in the interval from 40 to 50?20304050607002468101214Frequency
  4. Find how many more values lie from 0 to 10 than from 10 to 20.01020304050024681012Frequency
  5. How many of the data values fall below 40?20253035404502468101214Frequency

  1. Find a percent from a histogram

    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. Of the 25 cars, what percent were going 45 miles per hour or faster?30354045505502468Frequency
  2. A study recorded 20 reading times last week, in minutes, shown here in bars 10 wide. A bar counts its left edge but not its right. Find the percent of the 20 students that read for less than 70 minutes.30405060708002468Frequency
  3. The histogram shows 20 ages of people at a concert, in years, in intervals of 10; each bar includes its left edge but not its right. What percent of the 20 people are 40 or older?30405060708002468Frequency
  4. Here 25 quiz scores, in points, are drawn as a histogram with a bar width of 5; a value on a bar edge belongs to the bar on its right. What percent of the 25 students scored fewer than 30 points?2025303540450246810Frequency
  5. A histogram sorts 40 daily high temperatures, in degrees Fahrenheit, into intervals 5 wide, each counting its left endpoint and not its right. Of the 40 days, what percent reached 45 degrees or more?3035404550550246810Frequency

  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.1020304050600246810Frequency
  2. Skewed left, skewed right or symmetric? Use the shape to compare the mean and the median.304050607080900246810Frequency
  3. Is the distribution skewed left, skewed right or symmetric? Is the mean greater than, less than or about equal to the median?102030405060708002468Frequency
  4. Describe the shape of the histogram, and say whether the mean is greater than, less than or about equal to the median.607080901001101201300246810Frequency
  5. Skewed left, skewed right or symmetric? Use the shape to compare the mean and the median.2030405060708002468Frequency

  1. Find the interval with the median

    The histogram shows how many minutes each of 15 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?4050607080900246810Frequency
  2. A data set has 37 whole numbers, shown in the histogram. Each bar covers ten values and includes its left edge but not its right. In which interval does the median fall?30405060708002468Frequency
  3. The histogram shows the weights of 21 packages, in whole pounds. Each bar covers ten pounds and includes its left edge but not its right. Which bar holds the middle value, once the data are put in order?6070809010011002468Frequency
  4. 15 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 interval contains the median?506070809010002468Frequency
  5. The histogram shows the test scores of 21 students. Each bar covers ten scores and includes its left edge but not its right. Which interval contains the median?50607080901000123456Frequency

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

Sigma Prep · sigmaprep.io/worksheets

Name

HistogramsAnswer keyVersion 2

Date Period

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

  1. Read a histogram

    Count the values under 30. How many are there?20253035404502468101214Frequency15
  2. How many of the values lie between 10 and 30?01020304050024681012Frequency16
  3. How many more values are in the interval from 50 to 60 than in the interval from 40 to 50?20304050607002468101214Frequency5
  4. Find how many more values lie from 0 to 10 than from 10 to 20.01020304050024681012Frequency2
  5. How many of the data values fall below 40?20253035404502468101214Frequency31

  1. Find a percent from a histogram

    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. Of the 25 cars, what percent were going 45 miles per hour or faster?30354045505502468Frequency28%
  2. A study recorded 20 reading times last week, in minutes, shown here in bars 10 wide. A bar counts its left edge but not its right. Find the percent of the 20 students that read for less than 70 minutes.30405060708002468Frequency75%
  3. The histogram shows 20 ages of people at a concert, in years, in intervals of 10; each bar includes its left edge but not its right. What percent of the 20 people are 40 or older?30405060708002468Frequency60%
  4. Here 25 quiz scores, in points, are drawn as a histogram with a bar width of 5; a value on a bar edge belongs to the bar on its right. What percent of the 25 students scored fewer than 30 points?2025303540450246810Frequency40%
  5. A histogram sorts 40 daily high temperatures, in degrees Fahrenheit, into intervals 5 wide, each counting its left endpoint and not its right. Of the 40 days, what percent reached 45 degrees or more?3035404550550246810Frequency35%

  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.1020304050600246810FrequencySymmetric; 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.304050607080900246810FrequencySkewed 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?102030405060708002468FrequencySkewed right; the mean is greater than the median
  4. Describe the shape of the histogram, and say whether the mean is greater than, less than or about equal to the median.607080901001101201300246810FrequencySymmetric; the mean and the median are about equal
  5. Skewed left, skewed right or symmetric? Use the shape to compare the mean and the median.2030405060708002468FrequencySkewed left; the mean is less than the median

  1. Find the interval with the median

    The histogram shows how many minutes each of 15 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?4050607080900246810Frequency40–49
  2. A data set has 37 whole numbers, shown in the histogram. Each bar covers ten values and includes its left edge but not its right. In which interval does the median fall?30405060708002468Frequency50–59
  3. The histogram shows the weights of 21 packages, in whole pounds. Each bar covers ten pounds and includes its left edge but not its right. Which bar holds the middle value, once the data are put in order?6070809010011002468Frequency90–99
  4. 15 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 interval contains the median?506070809010002468Frequency80–89
  5. The histogram shows the test scores of 21 students. Each bar covers ten scores and includes its left edge but not its right. Which interval contains the median?50607080901000123456Frequency60–69

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

How to do these

Bars: 10–19 (3), 20–29 (7), 30–39 (6), 40–49 (4). What percent of the values are at least 30?

  1. There are 3 + 7 + 6 + 4 = 20 values.
  2. At least 30 means the last two bars: 6 + 4 = 10.
  3. 10 ÷ 20 = 0.5.

The answer is 50%.

Where students go wrong

Picking the middle bar as the interval with the median. With 13 values the median is the 7th, so add bar heights from the left until the running total reaches 7.

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.

Algebra 1 is usually taken around 8th or 9th 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.