7.03 Mean and median as measures of center
Describe what the mean measures for a set of scores.
Find the mean of the following data sets:
6, \, 4
8, \, 5
4, \, 10, \, 2, \, 9, \, 5
6, \, 14, \, 10, \, 13, \, 5, \, 9, \, 14, \, 15
4, 8, 9, 12
9, 7, 11, 4
5, 2, 3, 25
8, 5, 20, 4
8,\, 15,\, 6,\, 27,\, 3
56,\, 89,\, 95,\, 71,\, 75,\, 84,\, 65,\, 83
22.4,\, 25.4,\, 19.1,\, 24.3,\, 7.4
- 14,\, 0,\, - 2,\, - 18,\, - 8,\, 0,\, - 15,\, - 1
Determine whether each of the following data sets has a mean of 3:
8,\, 4,\, 2,\, 3,\, 1
3,\, 2,\, 5,\, 1,\, 4
1,\, 3,\, 7,\, 5,\, 2
2,\, 4,\, 5,\, 4,\, 3
Which two data sets have the same mean?
Data Set A: 11, 5, 14, 18, 15
Data Set B: 8, 14, 24, 7, 12
Data Set C: 13, 27, 9, 6, 8
Data Set D: 13, 15, 7, 17, 9
Find the sum of the following sets of scores:
A set of 10 scores with a mean of 4.
A set of 29 scores with a mean of 37.7.
A set of five numbers has a mean of 10. Two of the numbers are 6 and 13. Determine whether the following 3 other numbers could be in the set:
15,\, 11,\, 8
10,\, 13,\, 8
13, \,5,\, 6
10,\, 6,\, 18
The mean of a set of scores is 35 and the sum of the scores is 560. Calculate the number of scores in the set.
Victoria has scored 12 goals this season, with a mean of 2 goals per game. How many games did she play?
Five numbers have a mean of 7. If 4 of the numbers are 10, 10, 8 and 7 and the last number is x, find the value of x.
The mean of four scores is 21. If three of the scores are 17, 3 and 8, find the fourth score.
Han wants to try out as a batsman for a cricket team. In his last three matches, he scored 61, 75 and 66 runs. In his last match before trying out, he wants to lift his mean to 70.
If x is the number of runs he needs to score to achieve this, find the value of x.
The mean of a set of 41 scores is 18.6. If a score of 71.8 is added to the set, find the new mean. Round your answer to two decimal places.
A teacher calculated the mean of 25 students’ scores to be 64. A student who later completed the assessment got a score of 55. Find the new mean of the class, correct to two decimal places.
Find the median of the following data sets:
2, \, 3, \, 4, \, 5, \, 6
6, \, 9, \, 3, \, 5, \, 4
1, \, 4, \, 6, \, 8
2, \, 4, \, 9, \, 10
3, \, 18, \, 10, \, 19, \, 12, \, 5, \, 6, \, 20, \, 7
7, \, 19, \, 6, \, 14, \, 18, \, 11
5.3, \, 8.4, \, 2.6, \, 4.7, \, 3.5
49.4, \, 25.4, \, 47.2, \, 34.2, \, 28.4, \, 32.2
A set of 15 scores is arranged in increasing order. In what position does the median score lie?
Determine whether each data set has a median of 17.5:
15, 12, 17, 10
15, 22, 13, 18
22, 12, 19, 16
21, 10, 17, 14
Write down four consecutive odd numbers whose median is 12.
Write down four whole numbers whose median is 14 and whose range is 3.
Find the median from the following frequency distribution tables:
| Score | 12 | 13 | 14 | 15 | 16 |
|---|---|---|---|---|---|
| Frequency | 1 | 2 | 3 | 4 | 5 |
| Score | 15 | 16 | 17 | 18 | 19 |
|---|---|---|---|---|---|
| Frequency | 1 | 4 | 1 | 4 | 4 |
| Score | 15 | 16 | 17 | 18 | 19 |
|---|---|---|---|---|---|
| Frequency | 2 | 7 | 3 | 1 | 5 |
| Score | 11 | 14 | 19 | 22 | 29 |
|---|---|---|---|---|---|
| Frequency | 10 | 13 | 4 | 7 | 12 |
The television show "Dragon Duels" ran for three seasons, each with 6 episodes. The average fan ratings (out of 10) for each episode are shown in the following table:
| Episode 1 | Episode 2 | Episode 3 | Episode 4 | Episode 5 | Episode 6 | |
|---|---|---|---|---|---|---|
| Season 1 | 8.2 | 8.4 | 7.9 | 7.9 | 8 | 8.2 |
| Season 2 | 8.2 | 8.6 | 9.1 | 7.8 | 8.8 | 8.4 |
| Season 3 | 8.9 | 9.4 | 9.2 | 9.7 | 7.4 | 4.3 |
Which season has the greatest mean rating?
Which season has the greatest median rating?