Question

Income of 100 students of their parents is given as follows:

Income (in thousand Rs.)	No. of students (f)
0 – 8	8
8 – 16	35
16 – 24	35
24 – 32	14
32 – 40	8

Draw an ogive for the given distribution on a graph sheet. Use a suitable scale for your exercise. Use your ogive to estimate:

1. the median income.
2. Calculate the income below which freeship will be awarded to students if their parents income is in the bottom 15%
3. Mean income.

The incomes of the parents of 100 students in a class in a certain university are tabulated below.

Income (in thousand ₹)	0 – 8	8 – 16	16 – 24	24 – 32	32 – 40
No. of students	8	35	35	14	8

1. Draw a cumulative frequency curve to estimate the median income.
2. If 15% of the students are given freeships on the basis of the income of their parents, find the annual income of parents, below which the freeships will be awarded.
3. Calculate the Arithmetic mean.

Answer 1

i. Cumulative frequency curve

Income (in thousand Rs.)	No. of students (f)	Cumulative Frequency	Class Mark  x	fx
0 – 8	8	8	4	32
8 – 16	35	43	12	420
16 – 24	35	78	20	700
24 – 32	14	92	28	392
32 – 40	8	100	36	288
	`sumf = 100`			`sumfx = 1832`

We plot the points (8, 8), (16, 43), (24, 78), (32, 92) and (40, 100) to get the curve as follows:

Here, N = 100

`=> N/2 = 50`

At y = 50, affix A.

Through A, draw a horizontal line meeting the curve at B.

Through B, a vertical line is drawn which meets OX at M.

OM = 17.6 units

Hence, median income = 17.6 thousands

ii. 15% of 100 student = `(15 xx 100)/100 = 15`

From c.f. 15, draw a horizontal line which intersects the curve at P.

From P, draw a perpendicular to x-axis meeting it at Q which is equal to 9.6.

Therefore, freeship will be awarded to students provided annual income of their parents is upto 9.6 thousands.

iii. Mean = `(sumfx)/(sumf) = 1832/100 = 18.32`