Question

For one term, absentee record of students is given below. If mean is 15.5, then the missing frequencies x and y are.

Number of days	0 - 5	5 - 10	10 - 15	15 - 20	20 - 25	25 - 30	30 - 35	35 - 40	TOTAL
Total Number of students	15	16	x	8	y	8	6	4	70

विकल्प

• x = 4 and y = 3

• x = 7 and y = 7

• x = 3 and y = 4

• x = 7 and y = 6

Answer 1

x = 7 and y = 6

Explanation:-

Construct a table as follows:

Class interval	Frequency (fi)	Midpoint (xi)	fixi
0 - 5	15	2.5	37.5
5 - 10	16	7.5	120
10 - 15	x	12.5	12.5x
15 - 20	8	17.5	140
20 - 25	y	22.5	22.5y
25 - 30	8	27.5	220
30 - 35	6	32.5	195
35 - 40	4	37.5	150
Total	70		12.5x + 22.5y + 862.5

Mean = `(12.5x + 22.5y + 862.5)/70`

`⇒ 15.5 = (12.5x +22.5y + 862.5)/70`

`⇒ 15.5 xx 70 = 12.5x +22.5y + 862.5`

⇒ 12.5x + 22.5y = 222.5

⇒ 125x + 225y = 2225

⇒ 5x + 9y = 89         .....(i)

Also,

x + y + 57 = 70

x + y = 13          ......(ii)

Multiplying equation (ii) by 5 and then subtracting from (i) as,

5x + 9y = 89

5x + 5y = 65

4y = 24

y = 6

Substituting the value of y in equation (ii), we get

x + y = 13

⇒ x + 6 = 13

⇒ x = 7

Hence x = 7 and y = 6