Solutions of chapter 24. Measures of Central Tendency | RD Sharma - Mathematics

1

If the heights of 5 persons are 140 cm, 150 cm, 152 cm, 158 cm and 161 cm respectively, find the mean height.

2

Find the mean of 994, 996, 998, 1002 and 1000.

3

Find the mean of first five natural numbers.

4

Find the mean of all factors of 10.

5

Find the mean of first 10 even natural numbers.

6

Find the mean of x, x+2, x+4, x+6, x+8.

7

Find the mean of first five multiples of 3.

8

Following are the weights (in kg) of 10 new born babies in a hospital on a particular day:

3.4, 3.6, 4.2, 4.5, 3.9, 4.1, 3.8, 4.5, 4.4, 3.6

Find the mean

9

The percentage of marks obtained by students of a class in mathematics are:

64, 36, 47, 23, 0, 19, 81, 93, 72, 35, 3, 1

Find their mean.

10

The numbers of children in 10 families of a locality are:

2, 4, 3, 4, 2, 0, 3, 5, 1, 1, 5

Find the mean number of children per family.

11

If M is the mean of x₁, x₂, x₃, x₄, x₅ and x₆, prove that

(x₁-M)+ (x₂-M)+ (x₃-M)+ (x₄-M)+ (x₅-M)+(x₆-M) = 0.

12

Durations of sunshine (in hours) in Amritsar for first 10 days of August 1997 as reported by the Meteorological Department are given below:

9.6, 5.2, 3.5, 1.5, 1.6, 2.4, 2.6, 8.4, 10.3, 10.9

(i) Find the mean

(ii) Verify that = 0

13

Explain, by taking a suitable example, how the arithmetic mean alters by (i) adding a constant k to each term, (ii) subtracting a constant k from each them, (iii) multiplying each term by a constant k and (iv) dividing each term by a non-zero constant k.

14

The mean of marks scored by 100 students was found to be 40. Later on it was discovered that a score of 53 was misread as 83. Find the correct mean.

15

The traffic police recorded the speed (in km/h) of 10 motorists as 47, 53, 49, 60, 39, 42, 55, 57, 52, 48. Later on an error in recording instrument was found. Find the correct overage speed of the motorists if the instrument recorded 5 km/hr. less in each case.

16

The mean of five numbers is 27. If one number is excluded, their mean is 25. Find the excluded number.

17

The mean weight per student in a group of 7 students is 55 kg. The individual weights of 6 of them (in kg) are 52, 54, 55, 53, 56 and 54. Find the weight of the seventh student.

18

The mean weight of 8 numbers is 15. If each number is multiplied by 2, what will be the new mean?

19

The mean of 5 numbers is 18. If one number is excluded, their mean is 16. Find the excluded number.

20

The mean of 200 items was 50. Later on, it was discovered that the two items were misread as 92 and 8 instead of 192 and 88. Find the correct mean.

21

Find the values of n and in each of the following cases:

(i) = -10 and = 62

(ii) = 30 and = 150

22

The sums of the deviations of a set of n values x₁, x₂, x₃,…., x_nmeasured from 15 and -3 are -90 and 54 respectively. Find the value of n and mean.

23

Find the sum of the deviations of the variable values 3, 4, 6, 7, 8, 14 from their mean.

24

If is the mean of the ten natural numbers, x₁, x₂, x₃,…., x₁₀, show that

(x₁-)+(x₂-)+ ….+(x₁₀-)= 0.

1

Calculate the mean for the following distribution:

x :	5	6	7	8	9
f :	4	8	14	11	3

2

Find the mean of the following data:

x:	19	21	23	25	27	29	31
f :	13	15	16	18	16	15	13

3

Find the mean of the following data is 20.6. Find the value of p.

4

If the mean of the following data is 15. Find p.

x :	5	10	15	20	25
f :	6	p	6	10	5

5

Find the value of p for the following distribution whose mean is 16.6.

x:	8	12	15	p	20	25	30
f :	12	16	20	24	16	8	4

6

Find the missing value of p, for the following distribution whose mean is 12.58.

x:	5	8	10	12	p	20	25
f :	2	5	8	22	7	4	2

7

Find the missing frequency (p) for the following distribution whose mean is 7.68.

x:	3	5	7	9	11	13
f :	6	8	15	p	8	4

8

Find the value of p, if the mean of the following distribution is 20.

x:	15	17	19	20+p	23
f :	2	3	4	5p	6

9

Find the mean of the following distribution.

x:	10	12	20	25	35
f :	3	10	15	7	5

10

Candidates of four schools appear in a mathematics test. The data were as follows:

Schools

No. of Candidates

Average Score

I

II

III

IV

60

48

Not available

40

75

80

55

50

If the average score of the candidates of all the four school is 66, find the number of candidates that appeared from school III.

11

Five coins were simultaneously tossed 1000 times and at each toss the number of heads were observed. The number of tosses during which 0, 1, 2, 3, 4 and 5 heads were obtained are shown in the table below. Find the mean number of heads per toss.

No. of heads per toss

No. of tosses

0

1

2

3

4

5

38

144

342

287

164

25

Total

1000

12

Find the missing frequencies in the following frequency distribution if it is known that the mean of the distribution is 50.

x:	10	30	50	70	90
f :	17	f₁	32	f₂	19	Total 120.

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