Question

1. Find the mean of the following data :
(1) 40, 50, 65, 70, 75​

Answer 1

Answer

60

Explanation

Given ,

Sum of observation = 300

Number of observation = 5

$mean = \frac{300}{5}$

$==> mean = 60$

The mean of the given ungrouped data is 60

Answer 2

Answer:

Converting the given data into frequency distribution table

Maths marks No. of students

(f) Cf

60-65 8 8

65-70 12 20

70-75 14 34

75-80 8 42

80-85 5 47

85-90 6 53

90-95 4 57

Σf=57

Here, N=57

Hence the median class =

2

N

=

2

57

=28.5

In the above table 70-75 is the median class and the respective cf is 20 (nearest to the value of 28.5)

Acc to ques, l

1

=70 (lower limit of median class)

CF=20 (C= cumulative frequency preceding the median class)

i=l

2

−l

1

=5 (width of class interval of median class)

f = 14 (frequency of median class)

Median=l

1

+

f

2

N

−C

×i=70+

14

28.5−20

×5

Median= 73.05 (A)