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# Class 11 NCERT Solutions- Chapter 15 Statistics – Exercise 15.2

• Last Updated : 25 Feb, 2021

### Question 1. 6, 7, 10, 12, 13, 4, 8, 12

Solution:

We know,

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= 72/8

= 9 σ2 = (1/8) × 74

= 9.2

Therefore, Mean = 9 and Variance = 9.25

### Question 2. First n natural numbers

Solution:  = ((n(n + 1))2)/n

= (n + 1)/2 On substituting the value of mean, Substituting values of Summation On extracting common values, we have, σ2 = (n2 – 1)/12

Mean = (n + 1)/2 and Variance = (n2 – 1)/12

### Question 3. First 10 multiples of 3

Solution:

The required multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30.

We know, So, = (3 + 6 + 9 + 12 + 15 + 18 + 21 + 24 + 27 + 30)/10

= 165/10

= 16.5 = (1/10) × 742.5

= 74.25

Therefore, Mean = 16.5 and Variance = 74.25

### Question 4.

Solution:  = 760/40

= 19

Also, = (1/40) × 1736

= 43.4

### Question 5.

Solution:  = 2200/22

= 100 = (1/22) × 640

= 29.09

Therefore, Mean = 100 and Variance = 29.09

### Question 6. Find the mean and standard deviation using short-cut method.

Solution: Where A = 64, h = 1

So, = 64 + ((0/100) × 1)

= 64 + 0

= 64

Then, variance, σ2 = (12/1002) [100(286) – 02]

= (1/10000) [28600 – 0]

= 28600/10000

= 2.86

Hence, standard deviation = σ = √2.886

= 1.691

Therefore,

Mean = 64 and Standard Deviation = 1.691

### Question 7.

Solution:  = 3210/30

= 107 = (1/30) × 68280

= 2276

Therefore, Mean = 107 and Variance = 2276

### Question 8.

Solution:  = 1350/50

= 27 = (1/50) × 6600

= 132

Therefore, Mean = 27 and Variance = 132

### Question 9. Find the mean, variance and standard deviation using short-cut method

Solution: Where, A = 92.5, h = 5

So, = 92.5 + ((6/60) × 5)

= 92.5 + 0.5

= 92.5 + 0.5

= 93

Then, Variance, Standard deviation = σ = √105.583

= 10.275

### [Hint first make the data continuous by making the classes as 32.5-36.5, 36.5-40.5, 40.5-44.5, 44.5 – 48.5, 48.5 – 52.5 and then proceed.]

Solution: Where, A = 42.5, h = 4 = 42.5 + (25/100) × 4

= 42.5 + 1

= 43.5

Then, Variance, σ2 = (42/1002)[100(199) – 252]

On solving, we get,

= (1/625) [19900 – 625]

= 19275/625

= 771/25

= 30.84

Hence, standard deviation = σ = √30.84

= 5.553

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