April 13, 2023

Grouping Data

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2. Grouping discrete data.

April 13, 2023

You can often see a pattern more easily, if the data is grouped in some way.

Here is a list of the number of goals scored in each of the first 20 matches involving West Ham United, in the 2005 – 2006 season.

4 0 3 4 4 3 0 2 3 3 2 1 2 3 3 5 3 6 2 2

Number of goals Frequency0 21 12 53 74 35 16 1

From this table it is easy to identify the mode, the number of goals scored in a game with the greatest frequency.

The mode is 3.

You can also use this table to work out the mean.

73

Explanation

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Multiply each number of goals by its frequency, then add the results.

April 13, 2023

Mean

Number of goals Frequency Goals × Frequency0 2 01 1 12 5 103 7 214 3 125 1 56 1 6Totals 20 57

You can also use this table to work out the mean.

=57 ÷ 20= 2.85You can check this by adding up the original list of goals scored and dividing the answer by 20.

4 0 3 4 4 3 0 2 3 3 2 1 2 3 3 5 3 6 2 2

Explanation

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Multiply each number of goals by its frequency, then add the results.

April 13, 2023

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You can also use this table to work out the mean.

Number of goals Frequency0 21 12 53 74 35 16 1

This is called discrete data.This is because you can only score goals in whole, counted numbers.You cannot score 2.85 goals in a game!The mean, however can be a number it is not possible to score in real life.Other examples of discrete data would be:The number of people who live in your household.The number of students in your class with brown eyes.The number of blue cars in the car park.The number of fish in the sea.

Explanation

April 13, 2023

3 5 6 13 2

12 4 7 2 8

2 8 11 5 6

3 7 9 9 11

3 7 12 6 8

6 10 3 3 5

5 4 6 3 3

10 13 8 6 9

2 3 5 5 3

3 5 9 8 9

Shoe size Tally Frequency2

456789101112

A survey of the shoe sizes of 50 people produced the following results.Tally the results to produce a frequency table.

410

276355222

What is the modal group?

3

Shoe size 3.

Explanation

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April 13, 2023

Shoe size Tally Frequency Size × Freq.2

456789101112

410

276355222

3

Multiply shoe size by frequency, and total the column.Total the frequency column.

830

83536214045202224

50 315

31550

= 7.3Mean shoe size =

Explanation

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April 13, 2023

No. of Children FrequencyFrequency × No. of children

0 4

1 6

2 5

3 7

4 1

5 2

Total

Calculate the mean number of children in each house on Bury Road.

20 51

4

2110

60

10

5120

= 2.55Mean Children per house =

Example

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