Initial Diagnostic Audit - Unit E3: Measures of Central Tendency

Do NOT use a calculator for any questions in the audit unless specifically told otherwise
Section E3.1 - Mean, Medial, Mode and Range

The number of goals scored in each match in the Premier League one weekend was

1,  0,  4,  3,  1,  0,  5,  1,  3,  7

1. What is the mean number of goals scored per match?
2. What is the median number of goals scored per match?
3. What is the modal number of goals scored per match?
4. What is the range of the values?

5.
If a match was chosen at random, what is the probability that the number of goals  
scored is 3?
  
Section E3.2 - Finding the Mean from Tables and Tally Charts

You may use a calculator for questions in this section

The marks obtained by students on a short test are summarised below.

ScoreFrequency
0
  8
1
10
2
12
3
  3
4
  5
5
  2

6. How many students took the test?
7. Calculate the total of 'Scores × Frequency'.
8. What is the mean of the scores?
9. What is the median value?
10. What is the modal value?
Section E3.3 - Calculations with the Mean

You may use a calculator for questions in this section

11. The mean of a set of 5 numbers is 4.4. An extra number, 5, is added to the set.
What is the new mean?
12. In a cricket match, Richard's mean score in five innings was 52 runs.

(a) How many runs had he scored?

(b) After his next innings, his mean score was 54.
How many runs did he score in his sixth innings?

13. The mean of five numbers is 4.4, What extra number must be included to bring the mean up to 5.5?
14. The mean of seven numbers is 10.5. When an extra number is included, the mean changes to 10. What is the extra number?

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Produced by Russell Geach for CIMT - February 2013