The following is the distribution of height of students of a certain class in a city:
Height (in cm):
160-162
163-165
166-168
169-171
172-174
No of students:
15
118
142
127
18
Find the average height of maximum number of students.
Answers
SOLUTION :
★★Here, the data is not in continuous form( exclusive) so we convert it into continuous form (inclusive). For this subtract 0.5 from lower limit of each class interval and add 0.5 to upper limit of each class interval.
FREQUENCY DISTRIBUTION TABLE is in the attachment
Here the maximum frequency is 142, and the class corresponding to this frequency is 165.5 – 168.5 . So the modal class is 165.5 – 168.5 .
Therefore,l = 165.5, h = 168.5 – 165.5 = 3, f1 = 142, f0 = 118, f2 = 127
Mode = l + [(f1- f0) / (2f1- f0 - f2)] ×h
= 165.5+ [(142 - 118)/(2×142 - 118–127) ]×3
= 165.5 + [(24) /(284 - 245)×3
= 165.5 + [(24 × 3)/ 39
= 165.5 + 72/ 39
= 165.5 + 1.85
= 167.35 cm
Hence, the average height of maximum number of students is 167.35 cm .
MODE:
Mode is that value of the given observation which occurs most frequently.
Mode = l + (f1-f0/2f1-f0-f2) ×h
l = lower limit of the modal class
h = size of the class intervals
f1 = frequency of the modal class
f0 = frequency of the class preceding the modal class
f2 = frequency of the class succeed in the modal class.
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