The lengths of 40 leaves of a plant are measured correct to the

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 Multiple Choice QuestionsLong Answer Type

231.

The following table shows the ages of the patients admitted in a hospital during a year.

Find the mode and mean of the data given below. Compare and interpret the measures of central tendency.

Age (in yrs)

No. of patients

5-15

6

15-25

11

25-35

21

35-45

23

45-55

14

55-65

5

 
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 Multiple Choice QuestionsShort Answer Type

232.

The following data gives the information on the observed life-times (in hours) of 225 electrical components.

Life time (in hours)

Frequency

0-20

10

20-40

35

40-60

52

60-80

61

80-100

38

100-120

29

Determine the modal lifetimes of the components.

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 Multiple Choice QuestionsLong Answer Type

233.

The following data gives the distribution of total monthly household expenditure of 200 families of a village. Find the modal monthly expenditure of the families. Also, find the mean monthly expenditure:

Expenditure (in Rs.)

Number of families

1000-1500

24

1500-2000

40

2000-2500

33

2500-3000

28

3000-3500

30

3500-4000

22

4000-4500

16

4500-5000

7

 
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 Multiple Choice QuestionsShort Answer Type

234.

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/U.T.

15-20

3

20-25

8

25-30

9

30-35

10

35-40

3

40-45

0

45-50

0

50-55

2

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235.

The given distribution shows the number of runs scored by some top batsmen of the world in one-day international cricket matches.

Runs scored

Number of batsman

3000-4000

4

4000-5000

18

5000-6000

9

6000-7000

7

7000-8000

6

8000-9000

3

9000-10000

1

10000-11000

1

 

Find the mode of the data.
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236.

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

Numberof 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

 
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237.

The following frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Find the median, mean and mode of the data and compare them.

Monthly consumption of electricity (in units)

Number of consumers

68-85

4

85-105

5

105-125

13

125-145

20

145-165

14

165-185

8

185-205

4

 
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238.

If the median of the distribution given below is 28.5, find the values of x and y.

Class interval

Frequency

0-10

5

10-20

x

20-30

20

30-40

15

40-50

y

50-60

5

Total

x = 60

 
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239.

A life insurance agent found the folio wing data for distribution of ages of 100 policy holders. Calculate the median age, if policies are only given to persons having age 18 yrs. onwards but less than 60 years.

Age (in yrs.)

No. of policy holders

below 20

2

below 25

6

below 30

24

below 35

45

below 40

78

below 45

89

below 50

92

below 55

98

below 60

100

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240.

The lengths of 40 leaves of a plant are measured correct to the nearest millimetre and the data obtained is represented in the following table:

Length (in nun)

Number of leaves

118-126

3

127-135

5

136-144

9

145-153

12

154-162

5

163-171

4

172-180

2

Find the median length of the leaves.


We shall first convert the given data to continuous classes. Then, the data become

Length (in mm)

Number of leaves

Cumulative frequency

117.5-126.5

3

3

126.5-135.5

5

8

135.5-144.5

9

17

144.5-153.5

12

29

153.5-162.5

5

34

162.5-171.5

4

38

171.5-180.5

2

40

   

n = 40

 

We have n = 40. So,  open parentheses straight n over 2 close parentheses t h  
observation = 20th observation.

So, median lies in the group of 144.5 - 153.5 i.e.    median class = 144.5-153.5
Thus, we have

Median class = 144.5 - 153.5 = 144.5, straight n over 2=20, cf = 17, f=12 and h =10
Substituting these values in the formula of median we get

Median space equals straight l plus open square brackets fraction numerator begin display style straight n over 2 end style minus cf over denominator straight f end fraction close square brackets straight x space straight h space equals space 144.5 space plus open square brackets fraction numerator 20 minus 17 over denominator 12 end fraction close square brackets space straight x space 9
space space space space space space space space space space space equals space 144.5 space plus 3 over 12 straight x space 9 space equals space 144.5 space plus 9 over 4
space space space space space space space space space space space equals space 144.5 space plus space 2.25 space equals space 146.75 space mm
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