Mode, median and range worksheet

Part A: Working out and filling in

1. 1. 18

   The mode is the value seen most often. Which value appears more than once?

   18 appears twice and every other value once: 18, seen most often, is the mode.

2. 2. 20

   The data are already sorted, 5 values. Which place is right in the middle?

   5 values already in order: the middle one is the 3rd, 20.

3. 3. 28.5

   Sort first. With an even number of values there are two in the middle, and the median is halfway between them.

   Sorted, 6 values have two in the middle, 27 and 30. Median = (27 + 30) ÷ 2 = 28.5.

4. 4. 19

   Range = largest − smallest. In order, where are the largest and the smallest?

   The largest is 36 and the smallest 17: range = 36 − 17 = 19.

5. 5. 11

   □ is the largest. Find the smallest value first, then think: □ is 6 more than it.

   □ is the largest and 5 the smallest: □ − 5 = 6, so □ = 5 + 6 = 11.

6. 6. 1

   Find the tallest column. The mode is the value under it, not the number of dots.

   The tallest column, 7 dots, is over 1: the mode is 1 (the value, not the dots).

Part B: Choose, or true or false

1. 7. True

   Count how many times each value appears, then see whether 2 is the one seen most.

   2 appears 3 times, 16 twice and the rest once: the mode is 2.

2. 8. D

   In each plot, check every column's dots against 1, 0, 4, 2, 4.

   Each value needs as many dots as people: 1 over 0, 0 over 1… check each column.

3. 9. B. Discrete data

   Are goals counted or measured? Can a team score half a goal?

   Goals are counted, so they can only be whole numbers 0, 1, 2…: discrete data.

4. 10. C. Categorical data

   Do they give a number, or a name?

   Each person gives a name (a category), not a number: categorical data. You can only count how many are in each.

5. 11. C. The median

   See whether one value is unusually big. How does it affect the mean? Which one isn't pulled up by it?

   190 is an outlier. The median looks only at the middle value, 22, so it isn't dragged up: it describes a typical friend best.

6. 12. False

   The group 40–49 runs from 40 to 49, both included. Is 50 in that range?

   The group 40–49 runs from 40 to 49, both included; anything below 40 or above 49 is in another group.

Part C: Word problems

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

1. 13. 4

   The mode is the score that came up most. Find the biggest count first, then see which score it belongs to.

   A 4 came up 8 times, the most: the mode is the score 4, not how many times.

2. 14. 62 skips

   With the 8th friend there are 8 values. Which two are in the middle? Sort first.

   8 values sorted: the middle two are the 4th and 5th, 60 and 64; median (60 + 64) ÷ 2 = 62.

3. 15. 8°C

   Range = highest − lowest. Find the warmest and coldest days first.

   Warmest 11 °C, coldest 3 °C: 11 − 3 = 8 °C.

4. 16. 2 times

   Count all the dots first, work out which one is in the middle, then count from the left.

   23 people; the middle is the 12th dot. Counting from the left, it sits over 2.

5. 17. C. The number of people

   Of the three things, which one is a count in whole numbers?

   People are counted, only whole numbers: discrete data.

6. 18. 4 minutes

   Find the mean (total ÷ 5) and the median (the middle once sorted) separately, then take one from the other.

   Mean 120 ÷ 5 = 24, median 20: 24 − 20 = 4. The outlier 44 pulls the mean up.