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The median of the following data is 16. Find the missing frequencies a and b, if the total of the frequencies is 70.

The median of the data is 16. Find the missing frequencies a and b

Question 31 - CBSE Class 10 Sample Paper for 2021 Boards - Maths Standard - Part 2
Question 31 - CBSE Class 10 Sample Paper for 2021 Boards - Maths Standard - Part 3
Question 31 - CBSE Class 10 Sample Paper for 2021 Boards - Maths Standard - Part 4

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Note : This is similar to Example 8, Chapter 14 Class 10 Statistics (NCERT Book)

Check the answer here https:// www.teachoo.com /1963/561/Example-8---Median-is-525.-Find-values-of-x-and-y/category/Examples/

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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 βˆ‘β–’π’‡π’Š = 70 Finding Cummulative Freq. Since Median = 16 15 – 20 is median class Median = l + (𝑛/2 βˆ’π‘π‘“)/𝑓 Γ— h Where l = lower limit of median class h = class-interval n = βˆ‘β–’π‘“π‘– cf = cumulative freq.of class before median class f = frequency of the median class Now, Median = l + (𝒏/𝟐 βˆ’π’„π’‡)/𝒇 Γ— h 16 = 15 + (70/2 βˆ’ (24 + π‘Ž))/15 Γ— 5 16 βˆ’ 15 = (35 βˆ’ 24 βˆ’ π‘Ž)/3 1 = (11 βˆ’ π‘Ž)/3 3 = 11 βˆ’ a a = 11 βˆ’ 3 a = 8 Also, βˆ‘β–’π’‡π’Š = 55 + a + b 70 = 55 + a + b Putting a = 8 70 = 55 + 8 + b 70 = 63 + b 70 βˆ’ 63 = b b = 7

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