Question 31 The median of the following data is 16. Find the missing frequencies a and b, if the total of the frequencies is 70.Given
∑▒𝒇𝒊 = 70
Finding
Cummulative Freq.
Since
Median = 16
15 – 20 is median class
Median = l + (𝑛/2 −𝑐𝑓)/𝑓 × h
Where
l = lower limit of median class
h = class-interval
n = ∑▒𝑓𝑖
cf = cumulative freq.of class before median class
f = frequency of the median class
Now,
Median = l + (𝒏/𝟐 −𝒄𝒇)/𝒇 × h
16 = 15 + (70/2 − (24 + 𝑎))/15 × 5
16 − 15 = (35 − 24 − 𝑎)/3
1 = (11 − 𝑎)/3
3 = 11 − a
a = 11 − 3
a = 8
Also,
∑▒𝒇𝒊 = 55 + a + b
70 = 55 + a + b
Putting a = 8
70 = 55 + 8 + b
70 = 63 + b
70 − 63 = b
b = 7

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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