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# Probability and statistics : Post 16 Level 2 : Mathematics Content Knowledge

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Post 16 Level 2
Probability and statistics
Question 1 of 21

# 1. How confident are you that you can distinguish between using statistics to describe a population or a large data set and inferring properties of populations or distributions from a sample?

## Problem

A small firm has 10 employees. Here are their yearly salaries in thousands of pounds:

16, 16, 16, 16, 17, 18, 18, 19, 19, 45.

a) Calculate the mean, median and mode.

Prompt 1.

To find the mean: Add the salaries and divide by the number of employees.

To find the median: Make sure the salaries are in order of size. Find the middle salary.

To find the mode: Which salary do more employees get than any other?

b) Which of the mean, median or mode best represents the “average salary” of the employees.

Prompt 1.

Think about the mean: only one employee earns more than the mean so would it be sensible to use it to represent the average salary?

## Solution

a)

Mean = 16 + 16 + 16 + 16 + 17 + 18 + 18 + 19 + 19 + 4510 = 20

The mean salary is £20,000

Median: 16, 16, 16, 16, 17, 18, 18, 19, 19, 45.

The median is halfway between these two values. The median is £17500

The median salary is £17,500

Mode: There are 4 employees earning £16000, 1 earning £17000, 2 earning £18000, 2 earning £19000 and 1 earning £45000 therefore the mode is £16000.

b)

The mean is £20000. Only one employee earns more than £20000 and the other nine earn less than this. This would not be a good value to use to represent “average salary”.

The mode is £16000. This is at the low end of the salary scale and does not take into account employees who earn more than this. So this would not be a good value to use to represent “average salary”.

The median is £17500. Half the employees earn more than this and half earn less. The median is not affected very much by the very large salary that one employee gets. The median would be a good value to use to represent “average salary”.

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