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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