How to calculate the mean, mode and median

Premalatha nair

Measure

Set A2, 2, 3, 5, 5, 7, 8

Set B2, 3, 3, 4, 6, 7

The MeanTo find the mean, youneed to add up all thedata, and then dividethis total by the numberof values in the data.

Adding the numbers up gives:2 + 2 + 3 + 5 + 5 + 7 + 8 = 32There are 7 values, so you dividethe total by 7:    32 ÷ 7 = 4.57...

So the mean is 4.57 (2 d.p.)

Adding the numbers up gives:2 + 3 + 3 + 4 + 6 + 7 = 25There are 6 values, so you dividethe total by 6:    25 ÷ 6 = 4.166...

So the mean is 4.17 (2 d.p.)

MeasureSet A

2, 2, 3, 5, 5, 7, 8Set B

2, 3, 3, 4, 6, 7

The MedianTo find the median, youneed to put the valuesin order, then find themiddle value. If there aretwo values in the middlethen you find the meanof these two values.

The numbers in order:2 , 2 , 3 , (5) , 5 , 7 , 8The middle value is marked inbrackets, and it is 5.

So the median is 5

The numbers in order:2 , 3 , (3 , 4) , 6 , 7This time there are two values inthe middle. They have been putin brackets. The median is foundby calculating the mean of thesetwo values:    (3 + 4) ÷ 2 = 3.5

So the median is 3.5

MeasureSet A

2, 2, 3, 5, 5, 7, 8Set B

2, 3, 3, 4, 6, 7

The ModeThe mode is the valuewhich appears the mostoften in the data. It ispossible to have morethan one mode if thereis more than one valuewhich appears the most.

The data values:2 , 2 , 3 , 5 , 5 , 7 , 8The values which appear mostoften are 2 and 5. They bothappear more time than anyof the other data values.

So the modes are 2 and 5

The data values:2 , 3 , 3 , 4 , 6 , 7This time there is only one valuewhich appears most often - the number 3. It appears more timesthan any of the other data values.

So the mode is 3

MeasureSet A

2, 2, 3, 5, 5, 7, 8Set B

2, 3, 3, 4, 6, 7

The RangeTo find the range, youfirst need to find thelowest and highest valuesin the data. The range isfound by subtracting thelowest value from thehighest value.

The data values:2 , 2 , 3 , 5 , 5 , 7 , 8The lowest value is 2 and thehighest value is 8. Subtractingthe lowest from the highestgives:    8 - 2 = 6

So the range is 6

The data values:2 , 3 , 3 , 4 , 6 , 7The lowest value is 2 and thehighest value is 7. Subtractingthe lowest from the highestgives:    7 - 2 = 5

So the range is 5

ExampleA dice was rolled 20 times. On each roll the dice shows a value from 1 to 6.The results have been recorded in the table below:

Value Frequency

1 3

2 5

3 2

4 4

5 3

6 3

Number of times each value occurred

How do you get the mean?Value Frequency Value x F

1 3 1 × 3 = 3

2 5 2 × 5 = 10

3 2 3 × 2 = 6

4 4 4 x 4 = 16

5 3 5 x 3 = 15

6 3 6 x 3 = 18

Total 20 68

To get the mean: 68 divide by 20 =

3.4

How do you get the median?Value Frequency Value x F

1 3 1 × 3 = 3

2 5 2 × 5 = 10

3 2 3 × 2 = 6

4 4 4 x 4 = 16

5 3 5 x 3 = 15

6 3 6 x 3 = 18

Total 20 68

There are 20 values.. Middle value = 10 + 11

10th value = 3

(3+5+2=10)

11th value = 4

(3+5+2+4 =14)

Median = 3 + 4 = 3.5 _____

2

What is the mode?Value Frequency

1 3

2 5

3 2

4 4

5 3

6 3

The mode is 2 because it has the highest frequency

Practice

Encik Jeeva gave a test to a group of students. The table below shows the number of scores obtained by the students (30 students).40 35 44 65 68 90 87 92 20 44 67 54 41 54 34 67 71 45 69 56 45 67 34 34

42 56 78 79 50 40

value frequency V x F

20 1 20

34 3 102

35 1 35

40 2 80

41 1 41

42 1 42

44 2 88

45 2 90

50 1 50

54 2 108

56 2 112

65 1 65

67 3 201

68 1 68

69 1 69

71 1 71

78 1 78

79 1 79

87 1 87

90 1 90

92 1 92

Total 30 1668

• Mean = 1668 • ______• 30• • Median: middle number• 30 • __• 2• • = 15 and 16 • • = 54 •

Standard Deviation

s

Xi Each value

n Number of values in the data

x¯ Mean

Σ

How to calculate1. Find the average of the data set (x-)2. Take each value in the data set (x) and subtract

the mean from it to get (xi – x-)3. Square each of the differences (xi –x-)2 4. Add up all the results from step 3 to get the sum

of squares Σ(xi –x-)25. Divide the sum of squares by the numbers in the

data set minus one (n-1)6. Take the square root to get

example

Quiz scores: 1 3 5 7Mean = 16 /4 = 4

Substract squaring

1 1-4 -3 9

3 3-4 -1 1

5 5-4 1 1

7 7-4 3 9

20

• n = 4• n-1 = 3• • 20/3= 6.67 variance• Square root of 6.67 = 2.58 (standard

deviation)

• Statistics [Raw (Percent out of 50)]:• Mean: 34.09 (68.18%)• Median: 35 (70%)• Spread: 7.96 (15.92%)