From the data given below, find arithmetic mean and also show that
\(\sum _{ i=1 }^{ n }{ ({ x }_{ i }-\overline { x } ) } \) = 0

21

24

14

16

18

22

25

3

(a)

From the following data of the marks obtained by 60 students of a class mean was found to be 41 Show that \(\sum _{ i=1 }^{ n }{ F({ x }_{ i }-\overline { x } ) } =0\)

Marks	20	30	40	50	60	70
No of students	8	12	20	10	6	4

3

(a)

One sample has a mean of 6 and a second sample has a mean of 12. The two samples are combined into a single set of scores.
(a) What is the mean for the combined set if both of the original samples have n = 5 scores?
(b) What is the mean for the combined set if the first sample has n = 4 score and the second sample has n = 8?

3

(a)

There are 80 students in a class whose average marks in Statistics are 65. There are two sections in the class. In one section there are fifty students whose average marks are 62. Find the average marks of other section.

3

(a)

The average income of 20 employees in a factory was Rs 100. Later on it was discovered that the wages of two employees were wrongly recorded as 120 and 80 in place of 40 and 60. Find the correct mean.

3

(a)

Average age of 40 students in a class was 25 years. One student left the class whose age was 30 years. Find average age of remaining students.

3

(a)

Average marks of 50 students were 42. Later it was decided to give a grace of 2 marks to al students. Marks of all students were adjusted accordingly. Find new mean.

3

(a)

Average wages of 100 workers were 2000. One worker whose salary was 10000 left the job. What is average wage of remaining workers?

3

(a)

Find out the weighted mean from the data given below:

Variable	100	150	200	30	40
Weights	6	4	1	2	4

3

(a)

Comment on the performance of two colleges whose data are given below using simple and weighted mean. Which of the two is more useful in given situation?

Subject	College A		College B
	%	Total	%	Total
Commerce	71	3000	82	2000
Science	83	4000	76	3000
Humalities	73	5000	76	7000

3

(a)