Unit 2 – Measures of Central Tendency
Lesson 4 – Mean, Median, Mode and Range
Black – Mean, Median, Mode
Write down the mode for each of these sets of numbers.
1. {6, 8, 5, 3, 7, 4, 1, 6}
2. {7, 2, 6, 2, 1, 5, 7, 8, 3, 6, 9, 8, 1, 4, 3, 8}
3. {40, 53, 61, 29, 50, 8}
4. {50 c, $2, 20 c, $1, 5 c, 10 c, $5, $2, 20 c, $10}
5. This table shows distances from Auckland Airport to some destinations. These can all
be reached by direct flights.
Distances from Auckland Airport to selected overseas destinations
Destination
Distance
Adelaide
Apia
Bangkok
Brisbane
Buenos Aires
Hong Kong
Honolulu
Los Angeles
Melbourne
Nadi
Norfolk Island
Noumea
Pago Pago
Papeete
Destination
3 247
2 893
11 500
2 293
15 884
9 145
7 086
10 480
2 635
2 156
1 091
1 859
2 902
4 093
Perth
Port Moresby
Rarotonga
San Francisco
Santiago
Seoul
Singapore
Suva
Sydney
Taipei
Tokyo
Tonga
Townsville
Distance
5 400
4 126
3 013
10 503
12 822
12 869
8 410
2 141
2 158
10 654
8 837
2 004
3 359
a. Calculate the mean of these distances.
b. Calculate the median of these distances.
c. Which destination has the distance closest to the mean?
d. Which destination has the distance closest to the median?
6. Here are the temperatures (in degrees Celsius) recorded in eleven places in the
South Island on February 18 one year:
Ashburton
Alexandra
Blenheim
Christchurch
Dunedin
Invercargill
35
32
32
31
30
17
Greymouth
Nelson
Oamaru
Queenstown
Timaru
Calculate the mode temperature.
22
28
31
29
32
Unit 2 – Measures of Central Tendency
Lesson 4 – Mean, Median, Mode and Range
7. Here are the points scored by the 6th grade rugby team at Belleville High School in
their twelve games last season.
{34, 8, 0, 17, 22, 24, 35, 102, 39, 28, 0, 3}
a. Calculate the mean.
b. Calculate the mode.
c. Calculate the median.
d. Which average gives the most useful idea of how well the team scored over the
season?
8. Calculate the mean, median and mode of this set of numbers:
{6, 11, 7, 6, 6, 0}
9. Write down a set of five numbers that have a mean, mode, and median = 8. The
numbers must not all be the same.
10. A statistician has collected and weighed 149 items of data. The mean is 24 g, the
mode is 19 g, and the median is 23g. If one further item is collected, and has a
weight of 30 g, which average must get larger? Explain your choice.
A. the mean
C. the median
B. the mode
D. none of these
11. Four numbers have a mean of 6.5. What is their sum?
12. The Junior Girls Waterpolo team at Awarua College scored a mean of 11.25 points
per game last season. Altogether they played sixteen games. How many points did the
team score altogether?
13. Two brothers have a mean weight of 48 kg. If one of the brothers weighs 51 kg,
what does the other one weigh?
14. Wei-Li weighed some oranges. The mean weight was 345 g. The total weight was
2070 g. How many oranges did she weigh?
15. Tui has scored an average (mean) of 16 goals in the 5 games of netball she has played
this season. The number of goals she scored in the first 4 games are as follows: 18,
16, 13, 15. How many goals did she scored in her 5th game?
16. The average height of the starting five in the Bulls basketball team is 192 cm. If 4
of the players are 194 cm, 196 cm, 190 cm and 191 cm respectively, find the height
of the fifth player.
17. A bricklayer laid an average of 360 bricks per day for four days. How many bricks
would he need to lay on the fifth day to average 400 bricks per day for the five day
working week?
Unit 2 – Measures of Central Tendency
Lesson 4 – Mean, Median, Mode and Range
18. 20. Last week Shelly did homework on the following nights:
1 hours
2
Tuesday
1 1 hours
2
Wednesday 1 hour
Thursday
2 hours
Sunday
3 1 hours
2
Monday
2
Calculate the mean time spent doing homework on these five nights. Give the answer
in hours and minutes.
19. 21. There are seven judges watching competitors at a gymnastics competition. Here
are their scores for one competitor.
9.5
9.3
9.3
9.4
9.6
9.6
9.3
Calculate
a. the mode
b. the median
c. the mean
d. What is the value of the mean if the highest and lowest scores are not counted?
Solutions
1. 6
2. 8
3. No mode
4. Two modes - $2 and 20 c
5. 32
6. a. 6058
7. a. 26
b. 4093
b. 0
c. Perth
c. 23
d. Papeete
d. Median
8. 6
10. A
9. 5, 8, 8, 8, 11
11. 26
Unit 2 – Measures of Central Tendency
Lesson 4 – Mean, Median, Mode and Range
12. 180
13. 45 kg
14. 6
15. 18 goals
16. 189 cm
17. 560 bricks
18. 2 hours 6 minutes
19. a. 9.3
b. 9.4
c. 9.43
d. 9.42
Unit 2 – Measures of Central Tendency
Lesson 4 – Mean, Median, Mode and Range
Bibliography Information
Teachers attempted to cite the sources for the problems included in this problem set. In some cases,
sources may not have been known.
Problems
Bibliography Information
5 – 6, 12 - 14
Barton, David. Beta Mathematics. Pearson
Education New Zealand.
15 - 17
Barton, David. Gamma Mathematics
Pearson Education. New Zealand, 2000