Answer to Question #229869 in Statistics and Probability for Eugine

Question

 Dr Mukonda’s performance of his 270 Biostatistics class of students is given in an incomplete distribution below.

Variable 0-10 10-20 20-30 30-40 40-50 50-60 60-70

Frequency 12 21 f1 40 f2 26 21

(a) If the median is 35. Find the missing frequencies

(b) Draw the Histogram, the Line graph and pie chart hence explain statistically if these results are normally distributed

Answer 1

a) We use the formula

$Median=l+\frac{\frac{N}{2}-C}{f}\cdot h$

From data Median=35 therefore:

1.   Median class is 30-40;

2.   So we have f=40- frequency of median class;

3.   h=10- size of class interval;

4.   l=30- low limit of median class interval;

Thus we have

$Median=30+\frac{\frac{N}{2}-C}{40}\cdot 10=35$

5.   Therefore

6.   C=12+21+f₁=33+f₁ and we have N/2=53+f₁;

7.   Then N=106+2f₁=110+f₁+f₂;

8.   Sum of all frequencies  is not given, let we take N=170;

9.   In this case we will have N=170=106+2f₁=110+f₁+f₂;

and f₁=32,f₂=60-32=28;

b) Histogram:

Line Graph:

Pie Chart

Hence empirical distribution similar to normal by the form.