Averages from Frequency Tables · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Averages Without Writing the List Out

Mathematics · Data & Statistics · ages 14-15
Name ______________________   Date ____________

  1. A table lists values 1, 2, 3, 4 and 5 with frequencies 4, 7, 11, 6 and 2. What is the mode?

    • 3
    • 11
    • 5
    • 4

  2. A table of pets per household has its largest frequency, 12, beside the value 0. What is the mode?

    • 12
    • 0
    • 6, halfway between them
    • there is no mode when the answer is zero

  3. Twenty-five people are listed in order. Which position holds the median?

    • the 12th
    • the 12th and 13th together
    • the 13th
    • the 25th

  4. To find the mean from a frequency table, you add the value column and divide by the number of rows.

    Circle one:   True   False

  5. Leo works out a mean from a table of shoe sizes by adding 4 + 5 + 6 + 7 + 8 and dividing by 5. What has he missed?

    • He divided by 4 instead of by 5
    • He should have used the largest frequency
    • Shoe sizes cannot be averaged at all
    • Every size needs multiplying by its frequency first

  6. A frequency table's values multiplied by their frequencies add to 189, and the total frequency is 45. What is the mean?

    Answer: ______________

  7. A table has frequencies 8, 5, then one missing, then 7, and the total frequency is 31. What is the missing frequency?

    Answer: ______________

  8. Frequencies down a table read 6, 4, 9, 3, 3 for the values 0 to 4. Which value holds the 20th answer?

    • 1
    • 3
    • 4
    • 2

  9. Two Wren Lane groups answer the same question. Group A has a mean of 3.4 and a range of 2. Group B has a mean of 3.4 and a range of 9. What can you say?

    • Group B answered higher on average
    • The two groups gave identical answers
    • Group A must have had more members
    • They average the same, but B's answers are far more spread out

  10. A club's mean is 6 matches across 35 members. What is the total number of matches played?

    • 41
    • 5.83
    • 210
    • 35
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Answer key

For grown-ups. Fold this page away before handing over the rest.

Averages Without Writing the List Out W1-mt_5WF_Rhdb1X-s1

  1. 3 · The largest frequency is 11, and the value beside it is 3, so the mode is 3. The 11 counts people, the 5 is only the largest value on offer, and 4 is the range.
  2. 0 · The mode is the value that came up most, which is 0 pets. The 12 counts the households that gave that answer.
  3. the 13th · The median sits at position (25 + 1) / 2 = 13, and with an odd count that lands on a single person, the 13th.
  4. False · That treats every answer as if one person gave it. The frequencies say how many people are behind each value, so each value has to be multiplied by its frequency first.
  5. Every size needs multiplying by its frequency first · Leo averaged the five sizes on offer, not the people. If ten people wore a 6 and one wore an 8, those two sizes cannot count the same.
  6. 4.2 · The mean is the total of the values over the number of people: 189 / 45 = 4.2.
  7. 11 · The frequencies always add to the number of people, so the three known ones total 8 + 5 + 7 = 20 and the missing one is 31 - 20 = 11.
  8. 3 · The running totals are 6, 10, 19, 22, 25. The 20th passes 19 and is caught by 22, which is the row for the value 3.
  9. They average the same, but B's answers are far more spread out · The means match, so neither group sits higher on average. The ranges differ by a lot, so Group B holds answers much further apart than Group A's.
  10. 210 · The mean is the total divided by the members, so the total is the mean multiplied back: 6 × 35 = 210. Adding gives 41 and dividing gives 5.83, and neither is a total.
Worksheet · LightMySky