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?
Section E3.4 - Mean, Median and Mode for Grouped Data

You may use a calculator for questions in this section
Vicki investigated the times taken to serve 120 customers at Supermarket A. Her results are shown below.

Time (seconds)20 - 3030 - 4040 - 50 50 - 6060 - 70
Number of Customers
4
17
48
16
35

15. Calculate an estimate of the mean time to serve the customers. Give your answer to 1 d.p. s
16. What is the modal class for the serving times?
17. Estimate the median for the time. Give your answer to 1 d.p. s
Vicki decided to extend her investigation to Supermarket B. She obtained the times taken to serve 120 customers at Supermarket B. Her extended table is shown below.

Time (seconds)20 - 3030 - 4040 - 50 50 - 6060 - 70
Number of Customers at Supermarket A
4
17
48
16
35
Number of Customers at Supermarket B
5
20
54
36
5

Vicki correctly worked out the mean and modal class for the times at Supermarket B.
She also worked out correctly the median of the times for each supermarket.

18. Use your answers to questions 15, 16 and 17 to complete the table below.

Supermarket ASupermarket B
Median
46.5
Modal class
40 - 50
Mean
46.3
   
19. Which average in this table represents the data most fairly?

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Produced by Russell Geach for CIMT - February 2013