A teacher asks nine of his pupils how many pets they have at home. Here are the results. 1 1 1 2 3 4 5 7 111 (a) Work out the range of the nine results. (b) The median of the nine results is 3. The mean is 15. (i) Write down the mode. (ii) The teacher wants to use a sensible average to summarise the results. Which average should he use and why?

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A teacher asks nine of his pupils how many pets they have at home - OCR - GCSE Maths - Question 4 - 2020 - Paper 3

Question 4

A teacher asks nine of his pupils how many pets they have at home. Here are the results. 1 1 1 2 3 4 5 7 111 (a) Work out the range of the nine results. ... show full transcript

Worked Solution & Example Answer:A teacher asks nine of his pupils how many pets they have at home - OCR - GCSE Maths - Question 4 - 2020 - Paper 3

Step 1

Work out the range of the nine results.

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Answer

To find the range of the nine results, we first identify the smallest and largest values in the data set.

The smallest number is 1, and the largest number is 111.

The range can be calculated using the formula:

$\text{Range} = \text{Maximum} - \text{Minimum}$

Substituting the values gives:

$\text{Range} = 111 - 1 = 110$

Thus, the range of the nine results is 110.

Step 2

Write down the mode.

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Answer

The mode is the value that appears most frequently in a data set.

In the set of results: 1, 1, 1, 2, 3, 4, 5, 7, 111, 1 occurs three times, more than any other number.

Therefore, the mode is 1.

Step 3

Which average should he use and why?

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Answer

The teacher should use the median as the average to summarise the results because it is not affected by extreme values (outliers).

In this data set, the presence of 111 skews the mean upwards, making it less representative of the typical number of pets the pupils have. The median, which is 3, provides a better measure of central tendency for this data.

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