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.
May 21, 24 08:51 PM
May 21, 24 08:51 AM
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