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**Exercise 15.2**

**Find the mean and variance for each of the data in Exercises 1 to 5.**

**1. 6, 7, 10, 12, 13, 4, 8, 12**

**Ans. **Given: = 6, 7, 10, 12, 13, 4, 8, 12

= 6 + 7 + 10 + 12 + 13 + 4 + 8 + 12 = 72

And = 8 = 9

Also = 722

Variance =

=

= = 9.25

**2. First **** natural numbers**

**Ans. **Given: 1, 2, 3, 4, ………….,

And

Mean

Now, Variance =

=

=

=

=

**3. First 10 multiples of 3**

**Ans. **Given: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30

And

Mean

Now, Variance =

=

=

= = 74.25

**4. **

**Ans. **

Mean = = 19

Variance =

= = 43.4

**5. **

**Ans. **

Mean = = 22

Variance =

= = 29.09

**6. Find the mean and standard deviation using short cut method.**

**Ans. **

Mean = = 64

Variance =

=

= = = 1.69

**Find the mean and variance for the following frequency distribution in Exercises 7 and 8.**

**7. **

**Ans. **

Mean = = 107

Variance = = = 2280 – 4 = 2276

**8. **

**Ans. **

Mean

= = 25 + 2 = 27

Variance =

=

= = 132

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

**Ans. **

Mean

= = 92.5 + 0.5 = 93

Variance =

=

=

= = 105.58

Standard deviation = 10.27

**10. The diameters of circles (in mm) drawn in a design are given below:**

**Calculate the standard deviation and mean diameter of the circles.**

**[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 the proceed]**

Ans.

Mean

= = 42.5 + 1 = 43.5 mm

Standard deviation

=

= = 5.55

thanks sir

Thanks for giving such accurate and easy solution.

very helpful thanks