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.

Problem 5 :

Participants in a survey were asked how many foreign countries they had visited. The results are displayed in a vertical bar chart below.

a) Construct a frequency table from the graph

b) How many people took part in the survey ?

c) Calculate 

i) Mean     ii) Median     iii) Mode     iv) Range of the data

Solution :

a) 

b) Number of people took part in the survey = 6 + 8 + 5 + 4 + 2 + 1 + 2

= 28

c) Mean

= [0(6) + 1(8) + 2(5) + 3(4) + 4(2) + 5(1) + 6(2)]/28

= (0 + 8 + 10 + 12 + 8 + 5 + 12)/28

= 55/28

= 1.96

Median = (N + 1)/2^th term

= (28+1)/2^th term

= 29/2^th term

= 14.5^th term

= 15^th term

15^th term is 2.

Mode = Most number of people has visited 1 country.

Range = 8 - 1

= 7

Problem 6 :

A randomly selected sample of small business has been asked, how many full time employees are there in your business ? A bar chart has been constructed for the results.

a) How many small business gave data in the survey ?

b) How many of the business had only one or two full time employees?

c) What percentage of the business had five or more full time employees ?

d) Describe the distribution of the data ?

e) Find the mean of the data.

Solution :

a) Number of small business gave the data

= 6 + 9 + 12 + 9 + 6 + 4 + 2 + 1

= 49

b) Number of business had only one or two full time employees

= 6 + 9

= 15

c) Percentage of the business had five or more full time employees 

= (6+4+2+1)/49

= 13/49

Converting into percentage, we get

= (1/349) x 100%

= 26.53%

d) The distribution of the data is positively skewed.

e) mean = 49/15

= 3.2

Approximately 3.3