Find the mean of the following distribution by direct method.

Class interval	0-10	10-20	20-30	30-40	40-50
Number of workers	7	10	15	8	10

4

(a)

Using assumed mean method find the mean of the following frequency distribution.

Class	63-65	66-68	69-71	72-74	75-77
Frequency	4	3	7	8	3

4

(a)

Find the mode of given data.

Marks	0-10	10-20	20-30	30-40	40-50
Frequency	20	24	40	36	20

4

(a)

On sports day of a school, agewise participation of students is shown in the following distribution:

Age in years	5-7	7-9	9-11	11-13	13-15	15-17	17-19
Number of students	x	15	18	30	50	48	x

Find the mode of the data. Also, find missing frequencies when sum of frequencies is 181. 

4

(a)

The following table gives the literacy rate (in %) of 25 cities.

Literacy rate	50-60	60-70	70-80	80-90
Number of cities	9	6	8	2

Find the median class and modal class. 

4

(a)

During Medical check up of 200 students of school, their weights were recorded as follows:

Weight (in kg)	30-39	40-49	50-59	60-69	70-79	80-89
Number of students	5	22	63	74	30	6

Find the median weight of students. 

4

(a)

Consider the following distribution of daily wages of 50 workers of a factory:

Daily wages (in RS)	Number of workers
100-120	12
120-140	14
140-160	8
160-180	6
180-200	10

Find the mean daily wages of the workers of the factory by using an appropriate method.

4

(a)

In a retail market, fruit vendors were selling mangoes kept in packing boxes. These boxes contained varying number of mangoes. The following was the distribution of mangoes according to the number of boxes.

Number of mangoes	50-52	53-55	56-58	59-61	62-64
Number of boxes	15	110	135	115	25

 Find the mean of mangoes kept in a packing box. Which method of finding the mean did you choose?

4

(a)

The following table gives the literacy rate (in percentage) of 35 cities. Find the mean literacy rate.

Literacy rate (in %)	45-55	55-65	65-75	75-85	85-95
Number of cities	3	10	11	8	3

4

(a)

The following distribution gives the state-wise teacher-student ratio in higher secondary schools of India. Find the mode and mean of this data. Interpret the two measures.

Number of students per teacher	Number of states/UT
15-20	3
20-25	8
25-30	9
30-35	10
35-40	3
40-45	0
45-50	0
50-55	2

4

(a)

A student noted the number of cars passing through a spot on a road for 100 periods each of 3 min and summarised it in the table given below:

Number of cars	0-10	10-20	20-30	30-40	40-50	50-60	60-70	70-80
Frequency	7	14	13	12	20	11	15	8

 Find the mode of the data.

4

(a)

The following table gives the distribution of the lifetime of 400 neon lamps:

Lifetime (in hours)	Number of lamps
1500-2000	14
2000-2500	56
2500-3000	60
3000-3500	86
3500-4000	74
4000-4500	62
4500-5000	48

Find the median lifetime of a lamp. 

4

(a)

Following is the cumulative frequency distribution (of less than type) of 1000 persons each of age 20 yr and above. Determine the mean age.

Age (in years)	Below 30	Below 40	Below 50	Below 60	Below 70	Below 80
Number of persons	100	220	350	750	950	1000

4

(a)

The median class of a frequency distribution is 125-145. The frequency and cumulative frequency of the class preceding to the median class are 20 and 22, respectively. Find the sum of the frequencies, if the median is 137.

4

(a)

During the medical check-up 35 students of a class, their weights were recorded as follows:

Weight (in kg)	Number of students
Less than 38	0
Less than 40	3
Less than 42	5
Less than 44	9
Less than 46	14
Less than 48	28
Less than 50	32
Less than 52	35

Draw a 'less than type' ogive for the given data. Hence, obtain the median weight from the graph and verify the result by using the formula. What are benefits of regular medical check-up?

4

(a)