Worksheets · Statistics

Chi-square goodness of fit worksheet

The chi-square statistic measures how far observed counts sit from the counts a claim predicts. Square each difference, divide by the expected count, and add. A large total is evidence against the claim.

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

Sigma Prep · sigmaprep.io/worksheets

Name

Chi-Square Goodness of Fit

Date Period

Answer each question.

  1. Find the expected counts

    A sample of 280 is taken to test the claim that the categories occur in the proportions 35%, 20%, 45%. Find the expected count for each category.
  2. A sample of 160 is taken to test the claim that the categories occur in the proportions 35%, 15%, 20%, 20%, 10%. Find the expected count for each category.
  3. A sample of 380 is taken to test the claim that the categories occur in the proportions 30%, 15%, 30%, 25%. Find the expected count for each category.
  4. A sample of 180 is taken to test the claim that the categories occur in the proportions 40%, 20%, 40%. Find the expected count for each category.
  5. A sample of 400 is taken to test the claim that the categories occur in the proportions 25%, 10%, 40%, 25%. Find the expected count for each category.
  6. A sample of 320 is taken to test the claim that the categories occur in the proportions 15%, 25%, 25%, 15%, 20%. Find the expected count for each category.
  7. A sample of 220 is taken to test the claim that the categories occur in the proportions 20%, 15%, 65%. Find the expected count for each category.
  8. A sample of 200 is taken to test the claim that the categories occur in the proportions 25%, 15%, 40%, 20%. Find the expected count for each category.
  9. A sample of 140 is taken to test the claim that the categories occur in the proportions 25%, 15%, 35%, 20%, 5%. Find the expected count for each category.
  10. A sample of 240 is taken to test the claim that the categories occur in the proportions 40%, 10%, 50%. Find the expected count for each category.

  1. Find the chi-square statistic

    A die is rolled 72 times. The counts for 1 to 6 are 12, 8, 11, 9, 8, 24. Find the chi-square statistic, to the nearest hundredth.
  2. A spinner with 4 equal sections is spun 32 times. The counts are 10, 9, 4, 9. Find the chi-square statistic, to the nearest hundredth.
  3. A spinner with 5 equal sections is spun 65 times. The counts are 13, 8, 16, 17, 11. Find the chi-square statistic, to the nearest hundredth.
  4. A spinner with 5 equal sections is spun 85 times. The counts are 19, 17, 13, 16, 20. Find the chi-square statistic, to the nearest hundredth.
  5. A spinner with 4 equal sections is spun 44 times. The counts are 13, 15, 9, 7. Find the chi-square statistic, to the nearest hundredth.
  6. A die is rolled 102 times. The counts for 1 to 6 are 19, 18, 20, 12, 12, 21. Find the chi-square statistic, to the nearest hundredth.
  7. A spinner with 5 equal sections is spun 70 times. The counts are 18, 15, 15, 16, 6. Find the chi-square statistic, to the nearest hundredth.
  8. A spinner with 4 equal sections is spun 28 times. The counts are 8, 3, 10, 7. Find the chi-square statistic, to the nearest hundredth.
  9. A die is rolled 66 times. The counts for 1 to 6 are 7, 15, 6, 12, 13, 13. Find the chi-square statistic, to the nearest hundredth.
  10. A die is rolled 48 times. The counts for 1 to 6 are 10, 3, 7, 13, 7, 8. Find the chi-square statistic, to the nearest hundredth.

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

Sigma Prep · sigmaprep.io/worksheets

Name

Chi-Square Goodness of FitAnswer keyVersion 1

Date Period

Answer each question.

  1. Find the expected counts

    A sample of 280 is taken to test the claim that the categories occur in the proportions 35%, 20%, 45%. Find the expected count for each category.98, 56, 126
  2. A sample of 160 is taken to test the claim that the categories occur in the proportions 35%, 15%, 20%, 20%, 10%. Find the expected count for each category.56, 24, 32, 32, 16
  3. A sample of 380 is taken to test the claim that the categories occur in the proportions 30%, 15%, 30%, 25%. Find the expected count for each category.114, 57, 114, 95
  4. A sample of 180 is taken to test the claim that the categories occur in the proportions 40%, 20%, 40%. Find the expected count for each category.72, 36, 72
  5. A sample of 400 is taken to test the claim that the categories occur in the proportions 25%, 10%, 40%, 25%. Find the expected count for each category.100, 40, 160, 100
  6. A sample of 320 is taken to test the claim that the categories occur in the proportions 15%, 25%, 25%, 15%, 20%. Find the expected count for each category.48, 80, 80, 48, 64
  7. A sample of 220 is taken to test the claim that the categories occur in the proportions 20%, 15%, 65%. Find the expected count for each category.44, 33, 143
  8. A sample of 200 is taken to test the claim that the categories occur in the proportions 25%, 15%, 40%, 20%. Find the expected count for each category.50, 30, 80, 40
  9. A sample of 140 is taken to test the claim that the categories occur in the proportions 25%, 15%, 35%, 20%, 5%. Find the expected count for each category.35, 21, 49, 28, 7
  10. A sample of 240 is taken to test the claim that the categories occur in the proportions 40%, 10%, 50%. Find the expected count for each category.96, 24, 120

  1. Find the chi-square statistic

    A die is rolled 72 times. The counts for 1 to 6 are 12, 8, 11, 9, 8, 24. Find the chi-square statistic, to the nearest hundredth.15.50
  2. A spinner with 4 equal sections is spun 32 times. The counts are 10, 9, 4, 9. Find the chi-square statistic, to the nearest hundredth.2.75
  3. A spinner with 5 equal sections is spun 65 times. The counts are 13, 8, 16, 17, 11. Find the chi-square statistic, to the nearest hundredth.4.15
  4. A spinner with 5 equal sections is spun 85 times. The counts are 19, 17, 13, 16, 20. Find the chi-square statistic, to the nearest hundredth.1.76
  5. A spinner with 4 equal sections is spun 44 times. The counts are 13, 15, 9, 7. Find the chi-square statistic, to the nearest hundredth.3.64
  6. A die is rolled 102 times. The counts for 1 to 6 are 19, 18, 20, 12, 12, 21. Find the chi-square statistic, to the nearest hundredth.4.71
  7. A spinner with 5 equal sections is spun 70 times. The counts are 18, 15, 15, 16, 6. Find the chi-square statistic, to the nearest hundredth.6.14
  8. A spinner with 4 equal sections is spun 28 times. The counts are 8, 3, 10, 7. Find the chi-square statistic, to the nearest hundredth.3.71
  9. A die is rolled 66 times. The counts for 1 to 6 are 7, 15, 6, 12, 13, 13. Find the chi-square statistic, to the nearest hundredth.6.00
  10. A die is rolled 48 times. The counts for 1 to 6 are 10, 3, 7, 13, 7, 8. Find the chi-square statistic, to the nearest hundredth.7.00

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

How to do these

A die is rolled 60 times. The counts for 1 to 6 are 8, 12, 9, 11, 6, 14. Find the chi-square statistic, to the nearest hundredth.

  1. A fair die expects 60/6 = 10 of each face.
  2. Add (observed - expected)² / expected for all six faces.
  3. That is 42/10.

The answer is 4.20.

Where students go wrong

Dividing by the observed count instead of the expected one. The expected count is always the denominator.

Also called chi-square test, goodness of fit test or chi-squared.

What you can put on this worksheet

Expected counts
A sample of 260 is taken to test the claim that all 4 categories are equally likely. Find the expected count for each category. → 65, 65, 65, 65
The chi-square statistic
A spinner with 5 equal sections is spun 70 times. The counts are 17, 9, 14, 15, 15. Find the chi-square statistic, to the nearest hundredth. → 2.57

Questions about these worksheets

Yes. Every chi-square goodness of fit 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 chi-square goodness of fit 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 2: expected counts and the chi-square statistic. Tick as many as you want and set how many of each, or let it spread them evenly.

Dividing by the observed count instead of the expected one. The expected count is always the denominator.