HOW TO FIND MEAN AND STANDARD DEVIATION FROM BAR GRAPH

Find the mean and standard deviation from the bar graph given below.

Problem 1 :

standard-deviation-from-bar-graph-q1

Solution :

By observing the above bar graph, it is clear that

Values

4

5

6

7

8

9

10

11

12

Frequency

1

2

3

4

5

4

3

2

1

Standard deviation=Σ f(x-x)2Σ f
mean-and-standarad-deviation-frombar-graph-q1
Standard deviation = Σf(x -8)2Σf= 10025= 4= 2

The required,

mean = 8

and

standard deviation = 2

Problem 2 :

standard-deviation-from-bar-graph-q2.png

Solution :

By observing the above bar graph, it is clear that

Values

6

7

8

9

10

Frequency

2

6

9

6

2

Mean = 6(2)+7(6)+8(9)+9(6)+10(2)2+6+9+6+2= 20025= 8
standard-deviation-from-bar-graph-q2s.png
Standard deviation = Σf(x -8)2Σf= 3425= 1.36= 1.16

The required,

mean = 8

and

standard deviation = 1.16

Problem 3 :

standard-deviation-from-bar-graph-q3.png

Solution :

By observing the above bar graph, it is clear that

Values(x)

3

4

5

6

7

8

9

10

11

Frequency (f)

1

1

2

3

6

3

2

1

1

Mean = 3(1)+4(1)+5(2)+6(3)+7(6)+8(3)+9(2)+10(1)+11(1)1+1+2+3+6+3+2+1+1= 14020=
standard-deviation-from-bar-graph-q3s.png
Standard deviation = Σf(x -7)2Σf= 6820= 3.4=

The required,

mean = 7

and

standard deviation = 1.84

Problem 4 :

standard-deviation-from-bar-graph-q4.png

Solution :

By observing the above bar graph, it is clear that

Values (x)

3

4

5

6

7

Frequency (f)

1

4

10

4

1

Mean = 3(1)+4(4)+5(10)+6(4)+7(1)1+4+10+4+1= 10020= 5
standard-deviation-from-bar-graph-q4s.png
Standard deviation = Σf(x -5)2Σf= 1320=0.65=0.80

The required,

mean = 13

and

standard deviation = 0.80

Problem 5 :

standard-deviation-from-bar-graph-q5.png

Solution :

By observing the above bar graph, it is clear that

Number of employees (x)

1

2

3

4

5

6

7

8

Frequency (f)

6

9

12

9

6

4

2

1

standard-deviation-from-bar-graph-q5s.png
Standard deviation = Σf(x -3.5)2Σf= 146.2549= 2.98= 1.72

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