FINDING MEAN MEDIAN MODE AND RANGE FROM BAR GRAPH

Using the bar graph given below, find

(i) Mean   (ii)  Median    (iii) Mode   (iv) Range

Problem 1 :

Solution :

2 is repeated 3 times

3 is repeated 5 times

4 is repeated 3 times.

2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4

(i) Mean score = Sum of score /Total number of scores

Sum of scores = 3(2) + 5(3) + 3(4)

= 6 + 15 + 12

= 33

Total number of scores = 11

Mean score = 33/11

= 3

(ii)  Median score :

Number of scores = 11

median score = (11+1)/2^th

= 12/2

= 6^th score

Median score = 3

(iii) Mode :

3 is repeated 5 times. So, mode is 5.

(iv) Range :

Greatest score = 4, least score = 2

Range of scores = 4 - 2 ==> 2

Problem 2 :

Solution :

(i) Mean :

2 is repeated 1 time.

3 is repeated 5 times

4 is repeated 1 time

5 is repeated 1 time.

6 is repeated 3 times.

2, 3, 3, 3, 3, 3, 4, 5, 6, 6, 6

Mean score = Total score /total number of score 

Total score = 1(2) + 5(3) + 1(4) + 1(5) + 3(6)

= 2 + 15 + 4 + 5 + 18

= 44

Total number of scores = 11

Mean score = 44/11

= 4

(ii)  Median score :

= (11 + 1)/2 th score

= 6^th score

= 3

(iii) Mode :

3 is repeated 5 times. So, mode is 5.

(iv) Range :

Range score = Greatest score - least score

= 6 - 2

= 4

Problem 3 :

Solution :

1 is repeated 4 times

2 is repeated 2 times

3 is repeated 3 times 

4 is repeated 1 time

5 is repeated 1 time

6 is repeated 5 times.

1, 1, 1, 1, 2, 2, 3, 3, 3, 4, 5, 6, 6, 6, 6, 6

(i)  Mean :

Total score = 1(4) + 2(2) + 3(2) + 4(1) + 5(1) + 6(5)

= 4 + 4 + 6 + 4 + 5 + 30

= 53

Total number of scores = 16

Mean score = 53/16

= 3.3

(ii)  Median :

Total number of scores = 16

Median score = 16/2 ^th score

= 8^th score

= 3

(iii)  Mode :

6 is the most repeated score. So, mode is 6.

(iv) Range :

= Greatest score - smallest score

= 6 - 1

= 5

Problem 4 :

Solution :

(i) Mean :

1 is repeated 4 times

2 is repeated 2 times

3 is repeated 1 time

5 is repeated 5 times.

1, 1, 1, 1, 2, 2, 3, 5, 5, 5, 5, 5

Mean score = Total score / Total number of scores

= 1(4) + 2(2) + 3(1) + 5(5)

= 4 + 4 + 3 + 25

= 36

Total number of scores = 12

Mean score = 36/12

= 3

(ii) Median score :

Total number of scores = 12

median score = 12/2 ==> 6^th score

So, median score is 2.

(iii) Mode :

5 is the most repeated value. So, mode is 5.

(iv) Range :

= 5 - 1

= 4 is the range.