Maths (commerce) Solve the Following Question.(5 Marks)

The I.Q. test of 500 students of a college is as follows:

I.Q.	20-30	30-40	40-50	50-60	60-70	70-80	80-90	90-100
Number Of Student	41	52	64	180	67	45	40	11

Find graphically the number of students whose I.Q. is more than 55 graphically.

Determine graphically the value of median, D3, and P35 for the data given below:

Class	10-15	15-20	20-25	25-30	30-35	35-40	40-45
Frequency	8	14	8	25	15	14	6

Weight (Kg)	40-45	45-50	50-55	55-60	60-65	65-70	70-75	75-80
No. of persons	4	15	20	30	20	10	8	4

For the above data, find all quartiles and number of persons weighing between 57 kg and 72 kg.

Find Q1, D6 and P78 for the following data:

C.I.	8-8.95	9-9.95	10-10.95	11-11.95	12-12.95
F	5	10	20	10	5

Draw ogive of both the types for the following frequency distribution and hence find the median.

Marks	0-10	10-20	20-30	30-40	40-50	50-60	60-70	70-80	80-90	90-100
No. of students	5	5	8	12	16	15	10	8	5	2

In a college, there are 500 students in junior college, 5% score less than 25 marks, 68 scores from 26 to 30 marks, 30% score from 31 to 35 marks, 70 scores from 36 to 40 marks, 20% score from 41 to 45 marks and the rest score 46 and above marks. What are the median marks?

Draw an ogive for the following distribution. Determine the median graphically and verify your result by a mathematical formula.

Height (in cms.)	No. of students
145-150	2
150-155	5
155-160	9
160-165	15
165-170	16
170-175	7
175-180	5
180-185	1

Draw ogive for the following distribution and hence find graphically the limits of the weight of middle 50% fishes.

Weight Of Fishes (In gms)	800-890	900-990	1000-1090	1100-1190	1200-1290	1300-1390	1400-1490
No. Of Fishes	8	16	20	25	40	6	5

The following table gives the distribution of females in an Indian village. Determine the median age graphically.

Age Group	0-10	10-20	20-30	30-40	40-50	50-60	60-70	70-80	80-90	90-100
No. Of Females (In '000')	175	100	68	48	25	50	23	8	2	1

The following table shows the age distribution of heads of the families in a certain country. Determine the third, fifth, and eighth decile of the distribution graphically.

Age Of Head Of Famaily (In Years)	Numbers (Million)
Under 35	46
35-45	85
45-55	64
55-65	75
65-75	90
75 & Above	40

The following is the frequency distribution of overtime (per week) performed by various workers from a certain company. Determine the values of D2, Q2, and P61 graphically.

Overtime (In Hours)	Below -8	8-12	12-16	16-20	20-24	24-and Above
No. Of Workers	4	8	16	18	20	14

The following frequency distribution shows the profit (in ₹) of shops in a particular area of the city.

Profit per shop (in '000)	No. of shops
0-10	12
10-20	18
20-30	27
30-40	20
40-50	17
50-60	6

Find graphically
(i) the Unfits of middle 40% shops.
(ii) the number of shops having a profit of fewer than 35,000 rupees.

From the following distribution, determine the median graphically.

Daily wages (in ₹)	No. of employees
Above 300	520
Above 400	470
Above 500	399
Above 600	210
Above 700	105
Above 800	45
Above 900	7

The following table gives the distribution of daily wages of 500 families in a certain city.

Daily wages	No. of families
Below 100	50
100-200	150
200-300	180
300-400	50
400-500	40
500-600	20
600 above	10

Draw a ‘less than’ ogive for the above data. Determine the median income and obtain the limits of income of central 50% of the families.

Find graphically the values of D3 and P65 for the data given below:

I.Q. Of Students	69-69	70-79	80-89	90-99	100-109	110-119	120-129
No. Of Students	20	40	50	50	20	10	10

The weekly profit (in rupees) of 100 shops are distributed as follows:

Profit per shop	No. of Shops
0 -1000	10
1000-2000	16
2000-3000	26
3000-4000	20
4000-5000	20
5000-6000	5
6000-7000	3

Find the limits of the profit of middle 60% of the shops.

Calculate D4 and P48 from the following data:

Mid Value	2.5	7.5	12.5	17.5	22.5	Total
Fre-quency	7	18	25	30	20	100

From the following data calculate the rent of the 15th, 65th, and 92nd house.

House Rent (In ₹)	11000	12000	13000	15000	14000	16000	17000	18000
No. Of House	25	17	13	14	15	8	6	2

The following is the distribution of 160 workers according to the wages in a certain factory:

Wages More Than (in ₹)	No. Of Workers
8000	160
9000	155
10000	137
11000	103
12000	57
13000	23
14000	10
15000	1
16000	0

Determine the values of all quartiles and interpret the results.