Data and probability · Ages 14–15

Mean, median and mode worksheet

Part of: Measures of central tendency

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Data and probability · Ages 14–15

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

1.A shoe shop sold seven pairs one day, in sizes 39, 37, 41, 38, 42, 37, 40. What is the mode of the sizes?
Answer:
2.Seven households used 31, 20, 37, 29, 38, 25, 32 GB of mobile data in a month. What is the median, in GB?
Answer:
3.A basketball player scored 32, 20, 35, 27, 24 points in five games. How many points a game is that on average?
Answer:
4.A shoe shop sold seven pairs one day, in sizes 41, 39, 43, 40, 44, 39, 42. What is the mode of the sizes?
Answer:
5.The table shows how many bicycles each family on an estate owns (bicycles on the left, families on the right). How many bicycles does a family have on average?
Answer:
6.Five cars weigh 1079, 1081, 1081, 1077 and 1082 kg. What is their mean weight, in kg?
Answer:
7.A cruise terminal had 34, 25, 36, 17, 30, 34, 21, 27 thousand passengers on eight days. The mean is , the median and the mode .
Fill in each blank
Answer:
8.The stem-and-leaf diagram shows the ages (in years) of a hiking group's members. What is the median age?
Answer:
9.A cruise terminal had 44, 30, 55, 29, 40, 50, 30, 34 thousand passengers on eight days. The mean is , the median and the mode .
Fill in each blank
Answer:
10.The table shows how many times each player in a football squad was injured in a season (times on the left, players on the right). What is the median number of injuries?
Answer:

11.A website gained 18, 13, 26, 10, 17, 16 new members on six days. The mean of these data is greater than the median.
True or false?
Answer:
12.A website gained 18, 12, 33, 11, 15, 14 new members on six days. The mean of these data is greater than the median.
True or false?
Answer:

13.The stem-and-leaf diagram shows the ages (in years) of a badminton club's members. There are members, and the median age is .
Fill in each blank
Working:
Answer:
14.The table shows how many passengers each car in a car park carried (passengers on the left, cars on the right). What is the mode of the number of passengers?
Working:
Answer:
15.The table shows how many people live in each household on an estate (people on the left, households on the right). There are households and people in all, a mean of a household.
Fill in each blank
Working:
Answer:
16.A football team scored 3, 2, 4, 3, 4, 2, 3 goals in seven matches. That is goals in all, a mean of a match, and a median of .
Fill in each blank
Working:
Answer:
17.A football team scored 3, 1, 4, 3, 4, 2, 4 goals in seven matches. That is goals in all, a mean of a match, and a median of .
Fill in each blank
Working:
Answer:
18.A football team scored 2, 1, 3, 2, 3, 1, 2 goals in seven matches. That is goals in all, a mean of a match, and a median of .
Fill in each blank
Working:
Answer:

Show the answers and working

Mean, median and mode worksheet: Answers and working

1. 37
The mode is the value that comes most often: 37 comes twice, every other value once.
2. 31 GB
Put them in order first: the median of 7 is the (7 + 1) ÷ 2 = 4th, 31.
3. 27.6 points
The sum is 138; over 5 games, 138 ÷ 5 = 27.6 points.
4. 39
The mode is the value that comes most often: 39 comes twice, every other value once.
5. 2 bicycles
Each value times its frequency, added: Σfx = 44; total frequency 22: 44 ÷ 22 = 2.
6. 1080 kg
The sum 5400 ÷ 5 = 1080. Or assume a mean: pick a number near them, average the differences from it, and add that back.
7. 28, 28.5, 34
Mean 224 ÷ 8 = 28; in order, the median is the mean of the 4th and 5th, 28.5; 34, there twice, is the mode.
8. 52.5 years
A stem-and-leaf diagram is already in order: count the 12 values, and the median sits at place (12 + 1) ÷ 2: 52.5.
9. 39, 37, 30
Mean 312 ÷ 8 = 39; in order, the median is the mean of the 4th and 5th, 37; 30, there twice, is the mode.
10. 6
35 players, so the median sits at place (35 + 1) ÷ 2; add the counts from the top down to find the value there: 6.

11. True
Mean = 100 ÷ 6 = 503; in order, the median is the mean of the 3rd and 4th, 16.5.
12. True
Mean = 103 ÷ 6 = 1036; in order, the median is the mean of the 3rd and 4th, 14.5.

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

13. 10, 31
Count the leaves: 10. The data are in order, and the value at place (10 + 1) ÷ 2 is 31.
14. 2
The mode is the value with the highest frequency: 12 cars carried 2 passengers.
15. 25, 123, 4.92
Total frequency 25; Σfx = 123; 123 ÷ 25 = 4.92.
16. 21, 3, 3
The sum is 21; 21 ÷ 7 = 3; in order, the 4th, 3, is the median.
17. 21, 3, 3
The sum is 21; 21 ÷ 7 = 3; in order, the 4th, 3, is the median.
18. 14, 2, 2
The sum is 14; 14 ÷ 7 = 2; in order, the 4th, 2, is the median.

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