Data and charts · Ages 10–11

The median worksheet

Part of: Mode, median and range

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Data and charts · Ages 10–11

Numsprite
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Name:Date:Score:／48

Write each answer in the space. For word problems, show your working and write a sentence answer.

1.Data in order from smallest to largest: 8, 16, 18, 22, 30. What is the median?
Answer:
2.11 values are sorted from smallest to largest. Counting from the smallest, in which place is the median?
Answer:
3.41 values are sorted from smallest to largest. Counting from the smallest, in which place is the median?
Answer:
4.Data in order from smallest to largest: 17, 20, 24, 25, 26. What is the median?
Answer:
5.Data: 25, 32, 19, 28, 28, 16. What is the median?
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6.Data: 21, 26, 15, 26, 25, 26, 19. What is the median?
Answer:
7.Data: 11, 18, 5, 17, 15, 5. What is the median?
Answer:
8.Data: 15, 21, 5, 27, 15, 27, 9. What is the median?
Answer:

13.7 friends' skipping scores in a minute: 61, 73, 49, 82, 67, 75, 57. An 8th friend scores 94, more than everyone else. What is the median of the 8 scores?
Working:
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14.4 friends' savings, from least to most, are $29, $37, $ and $50. The median is $39.5. What is ?
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15.How long Ka-yan's MTR ride to Grandma's took each day for a week (minutes): 40, 24, 30, 40, 25, 24, 35. What is the median time in minutes?
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16.The heights of Ka-yan and 5 friends (cm): 138, 143, 138, 140, 138, 136. What is the median height of the 6 in cm?
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17.How long Ka-yee's MTR ride to Grandma's took each day for a week (minutes): 40, 40, 33, 40, 28, 40, 35. What is the median time in minutes?
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18.4 friends' savings, from least to most, are $14, $20, $ and $27. The median is $22.5. What is ?
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Answer:

Show the answers and working

The median worksheet: Answers and working

1. 18
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, 18.
2. 6
There are as many values before the median as after. Taking the median out of 11, how many are on each side?
The (11 + 1) ÷ 2 = 6th: 5 values come before it and 5 after.
3. 21
There are as many values before the median as after. Taking the median out of 41, how many are on each side?
The (41 + 1) ÷ 2 = 21st: 20 values come before it and 20 after.
4. 24
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, 24.
5. 26.5
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, 25 and 28. Median = (25 + 28) ÷ 2 = 26.5.
6. 25
Sort the values from smallest to largest, count them, then find the one in the middle.
Sort first: 15, 19, 21, 25, 26, 26, 26. With 7 values the middle is the 4th: 25.
7. 13
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, 11 and 15. Median = (11 + 15) ÷ 2 = 13.
8. 15
Sort the values from smallest to largest, count them, then find the one in the middle.
Sort first: 5, 9, 15, 15, 21, 27, 27. With 7 values the middle is the 4th: 15.

9. D. 31
The median needs sorting first: it isn't just whichever value is written in the middle.
Sort first: 17, 22, 31, 34, 35. The middle one is 31.
10. False
Sort first. With an even number of values, the median is halfway between the middle two. Then compare with 20.
Sorted, the two middle values are 15 and 20; the median is halfway between them: 17.5.
11. False
Sort first. With an even number of values, the median is halfway between the middle two. Then compare with 23.
Sorted, the two middle values are 19 and 23; the median is halfway between them: 21.
12. C. 20
The median needs sorting first: it isn't just whichever value is written in the middle.
Sort first: 15, 17, 20, 23, 28. The middle one is 20.

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

13. 70 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, 67 and 73; median (67 + 73) ÷ 2 = 70.
14. 42 dollars
The median is halfway between the middle two, 37 and □, so 37 + □ is twice the median.
The median is halfway between the middle two: 37 + □ = 39.5 × 2 = 79, so □ = 79 − 37 = 42.
15. 30 minutes
Sort the week's times from smallest to largest, then find the one in the middle.
Sorted: 24, 24, 25, 30, 35, 40, 40; the middle, 4th, is 30.
16. 138 cm
6 is an even number, so two people are in the middle. Sort the heights first.
Sorted, the middle two are 138 cm and 138 cm: (138 + 138) ÷ 2 = 138 cm.
17. 40 minutes
Sort the week's times from smallest to largest, then find the one in the middle.
Sorted: 28, 33, 35, 40, 40, 40, 40; the middle, 4th, is 40.
18. 25 dollars
The median is halfway between the middle two, 20 and □, so 20 + □ is twice the median.
The median is halfway between the middle two: 20 + □ = 22.5 × 2 = 45, so □ = 45 − 20 = 25.

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