Quartiles by using normal distribution

1. NADEEM UDDIN
ASSOCIATE PROFESSOR
OF STATISTICS
https://www.slideshare.net/NadeemUddin17
https://nadeemstats.wordpress.com/listofbooks/
QUARTILES BY USING NORMAL
DISTRIBUTION

3. Example-10
In a normal distribution with µ = 100 and σ = 15 find 𝑄1 𝑎𝑛𝑑𝑄3
Solution:
(a)
𝑄1 = First quartile, (the points below which 25% area lies and above
which 75% area lies)
ThusP(X ≤ 𝑄1) = 0.25
𝑃
𝑥−𝜇
𝜎
≤
𝑄1−𝜇
𝜎
= 0.25
𝑃 𝑍 ≤
𝑄1−100
15
= 0.25
𝑃 𝑍 ≤ −0.67 = 0.25
(from Z- table)

4. Hence
𝑄1 − 100
15
= −0.67
𝑄1 = 100 − (0.67)(15)
𝑄1 = 89.95
and
𝑄3 = Third quartile, (the points below which 75% area lies and
above which 25% area lies)
Thus P(X ≤ 𝑄3) = 0.75
𝑃
𝑥−𝜇
𝜎
≤
𝑄3−𝜇
𝜎
= 0.75
𝑃 𝑍 ≤
𝑄3−100
15
= 0.75
𝑃 𝑍 ≤ 0.67 = 0.75
(from Z- table)

5. Hence
𝑄3 − 100
15
= 0.67
𝑄3 = 100 + (0.67)(15)
𝑄3 = 110.05