If the arithmetic mean of the data given below is 28, find (a) the missing frequency, and (b) the median of the series:

Profit per retail shop (in Rs)

0 – 10

10 – 20

20 – 30

30 – 40

40 – 50

50 – 60

Number of retail shops

12

18

27

17

6

 

(i) Let the missing frequency be f1 

Arithmetic Mean = 28

 

 

Profit per Retail Shop (in Rs)

No of Retail Shops

Mid Value

 

Class Interval

(f)

(m)

fm

0 – 10

12

5

60

10 – 20

18

15

270

20 – 30

27

25

675

30 – 40

f1

35

35f1

40 – 50

17

45

765

50 – 60

6

55

330

 

 

 

or, 2240 + 28f1 = 2100 + 35f1

or, 2240 – 2100 = 35f1 – 28f1

or, 140 = 7f1

f1 = 20

 

(ii)

 

Class Interval

Frequency

 

(f)

Cumulative

Frequency

(CF)

 

0 – 10

12

12

 

10 – 20

18

30

 

20 – 30

27

57

 

30 – 40

20

77

 

40 – 50

17

94

 

50 – 60

6

100

 

Total

 

 

So, the Median class = Size of  item

                                         = 50th item

50th item lies in the 57th cumulative frequency and the corresponding class interval is 20 – 30.

 

  • 12
What are you looking for?