Compute the median for the following cumulative frequency distribution : weight in kg less than 38 less than 40 less than 42 less than 44 less than 46 less than 48 less than 50 less than 50 , number of students 0 , 3 , 5 , 9 , 14 , 28 , 32 , 35
Answers
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48.25 is the median for the given frequency distribution.
Step-by-step explanation:
Weight Frequency Midpoint Cumulative Frequency
(class) (No. of students) less than more than
38 - 40 3 39 3 123 + 3 = 126
40 - 42 5 41 8 118 + 5 = 123
42 - 44 9 43 17 109 + 9 = 118
44 - 46 14 45 31 95 + 14 = 109
46 - 48 28 47 59 67 + 28 = 95
48 - 50 32 49 91 35 + 32 = 67
50 - 52 35 51 126 35
∑f = N = 126
N/2 = 126/2 = 63
∵ Median class = 48 - 50
l = 48
f = 32
h = 2
c.f = 59
{ ℓ = lower limit of median class interval
C.f. = cumulative frequency preceding the median class frequency
f = frequency of the class interval to which median belongs
h = width of the class interval}
Median = ℓ + (N/2–C.f.)/f ×h
= 48 + (63 - 59)/32 * 2
= 48.25
∵ 48.25 is the median.
Learn more: calculate the median
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