Question

2. Calculate quartiles and third decile from the following data:
Central size : 2.5 7.5 12.5 17.5 22.5
Frequency : 7 18 25 30 20
(Ans. Q1 = 10, Q2 = 15, Q3 = 19.16, D3 = 11]​

Answer 1

Given: Central size : 2.5 7.5 12.5 17.5 22.5

           Frequency : 7 18 25 30 20

To Find: Calculate quartiles and third decile

Solution:

Sum of frequency (N)= 7+18+25+30 +20

N= 100

First to find the quartiles

Lower Quartile (Q1) = (N+1) * 1 / 4. = 10

Middle Quartile (Q2) = (N+1) * 2 / 4.= 15

Upper Quartile (Q3)= (N+1) * 3 / 4. =19.16

D3 = Value of 3 (30 + 1) / 10= 11

Therefore, Q1 = 10, Q2 = 15, Q3 = 19.16 and D3 = 11

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