1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# Calculate upper and lower quartile from the following data: Variable 0−10 10−20 20−30 30−40 40−50 50−60 60−70 Frequency 10 20 35 40 25 25 15

Open in App
Solution

## Class Interval Frequency (f) Cumulative Frequency (c.f.) 0 − 10 10 − 20 10 20 10 30 20 − 30 35 65 Q1 30 − 40 40 105 40 − 50 25 130 Q3 50 − 60 60 − 70 25 15 155 170 N=170 ${Q}_{1}=\mathrm{Size}\mathrm{of}{\left(\frac{\mathrm{N}}{4}\right)}^{\mathrm{th}}\mathrm{item}={\left(\frac{170}{4}\right)}^{\mathrm{th}}=42.{5}^{\mathrm{th}}\mathrm{item}$ This lies in the class interval (20-30). Now, ${Q}_{1}={l}_{1}=\frac{\frac{N}{4}-c.f.}{f}×i\phantom{\rule{0ex}{0ex}}\mathrm{or},{Q}_{1}=20+\frac{42.5-30}{35}×10\phantom{\rule{0ex}{0ex}}⇒{Q}_{1}=23.57\phantom{\rule{0ex}{0ex}}\mathrm{Thus},\mathrm{the}\mathrm{value}\mathrm{of}\mathrm{lower}\mathrm{quartile}\mathrm{is}23.57.\phantom{\rule{0ex}{0ex}}{Q}_{3}=\mathrm{Size}\mathrm{of}3{\left(\frac{170}{4}\right)}^{\mathrm{th}}=127.{5}^{\mathrm{th}}\mathrm{item}\phantom{\rule{0ex}{0ex}}\mathrm{This}\mathrm{lies}\mathrm{in}\mathrm{the}\mathrm{class}\mathrm{interval}\left(40-50\right).\phantom{\rule{0ex}{0ex}}{Q}_{3}={l}_{1}=\frac{3\left(\frac{N}{4}\right)-c.f.}{f}×i\phantom{\rule{0ex}{0ex}}\mathrm{or},{Q}_{3}=40+\frac{127.5-105}{25}×10\phantom{\rule{0ex}{0ex}}⇒{Q}_{3}=49\phantom{\rule{0ex}{0ex}}\mathrm{Thus},\mathrm{the}\mathrm{value}\mathrm{of}\mathrm{upper}\mathrm{quartile}\mathrm{is}49.$

Suggest Corrections
4
Join BYJU'S Learning Program
Related Videos
Cumulative Frerquency
MATHEMATICS
Watch in App
Explore more
Join BYJU'S Learning Program