Answer to Question #156714 in Statistics and Probability for Eugine Haweza

Question

Mr Mukonda’s perfomance of his 170 Biostatistics class of students is given in an incomplete distribution below.

Variable. Frequence

0-10 12

10-20. 21

20-30 f1

30-40 40

40-50 f2

50-60 26

60-70 18

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

(b) From Rusangu passing mark policy, explain if these results are normally distributed

Answer 1

Solution:

$\sum f =170$

$12+21+f1+40+f2+26+18=170$

$$117+f1+f2=170$$ $$f1+f2 =53 \space ...... (i)$$

The median class is 30-40:

$$M= L+ ({{N \over 2}-cf \over f}) i$$

$$35= 30 + ({85-(33+f1) \over 40})10$$ $$5={52-f1 \over 4}$$

$$20=52-f1 \therefore f1=32$$ $$f1+f2=53 \therefore f2=21$$

$Ans: f1=32 \space and \space f2=21$

b). Since the data is clearly bell shaped with largest values lying in the middle while smallest values lie towards the extremes, we can assume that the data is normally distributed