Answer to Question #326173 in Statistics and Probability for Robera

Question

a) Determine the missing frequencies of the following distribution given that the median

is 33.5 and themode is 34.0.

Class limits 0-9 10-19 20-29 30-39 40-49 50-59 60-69 Total

Freq. 4 16 f3 f4 f5 6 4 230

b) Compute the arithmetic mean.

c) Compute the value below which 25% of the observations lie.

d) Compute the value above which 25% of the observations lie

Answer 1

a. missing frequencies

Cumulative Frequency total = 30+f3+f4+f5=230

f3+f4+f5=200...........(i)

median class is 29.5 - 39.5

$33.5=29.5+[\frac{230/2-(20+f3)}{f4}]x10$

$0.4=(95-f3)/f4$

modal class is 29.5 - 39.5

$34=29.5+\frac{f4-f3}{(f4-f3)+(f4-f5)}x10$

0.45(2f4−f3−f5)=f4−f3

−0.1f4+0.55f3−0.45f5=0

$f3=55$

$f4=100$

$f5=45$

b) Arithmetic mean

$Arithmetic\ mean=\frac{(4x4.75)+(16x14.5)+(55x24.5)+(100x34.5)+(45x44.5)+(6x54.5)+(4x64.5)}{230}=33.3$

c) value below 25%

25/100x230=57.5

d) value above 25% + Value below 25% =100%. So

100%-57.5%=42.5%