# Statistics

**Exercise 1**

Find the mean deviation about the mean for the data in Exercises 1 and 2.

**1. **1. 4, 7, 8, 9, 10, 12, 13, 17

**2.** 38, 70, 48, 40, 42, 55, 63, 46, 54, 44

Find the mean deviation about the median for the data in Exercises 3 and 4.

**3.** 3. 13, 17, 16, 14, 11, 13, 10, 16, 11, 18, 12, 17

**4.** 4. 36, 72, 46, 42, 60, 45, 53, 46, 51, 49

Find the mean deviation about the mean for the data in Exercises 5 and 6.

Find the mean deviation about the median for the data in Exercises 7 and 8.

Find the mean deviation about the mean for the data in Exercises 9 and 10.

**11. **Find the mean deviation about median for the following data:

**12. **Calculate the mean deviation about median for the age distribution of 100 persons given below:

**Exercise 2**

Find the mean and variance for each of the data in Exercises 13 to 17.

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

**14. **First n natural numbers

**15.** First 10 multiples of 3

**16.** x_{i} 6 10 14 18 24 28 30

f_{i} 2 4 7 12 8 4 3

**17. **x_{i} 92 93 97 98 102 104 109

f_{i} 3 2 3 2 6 3 3

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

x_{i} 60 61 62 63 64 65 66 67 68

f_{i} 2 1 12 29 25 12 10 4 5

Find the mean and variance for the following frequency distribution in Exercises 19 and 20.

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

**22.** 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, 40.544.5, 44.5-48.5, 48.5-52.5 and then proceed]

**Exercise 3**

**23.** From the data given below state which group is more variable, A or B:

**24.** From the prices of shares X and Y below, find out which is more stable in value:

**25. ** An analysis of monthly wages paid to workers in two firms A and B, belonging to the same industry, gives the following results:

(i) Which firm A or B larger amount as monthly wages?

(ii) Which firm A or B shows greater variability in individual wages?

**26.**The following is the record of goals scored by team A in a football session:

For the team B, mean number of goals scored per match was 2 with a standard deviation 1.25 goals. Find which team may be considered more consistent?

**27. ** The sum and sum of squares corresponding to lengths (in cm) and weight (in gm) of 5- plant products are given below:

Which is more varying, the length or weight?

**Exercise 4**

**28.** The mean and variance of eight observations are 9 and 9.25 respectively. If six of the observations are 6, 7, 10, 12, 12 and 13, find the remaining two observations.

**29.** The mean and variance of 7 observations are 8 and 16 respectively. If five of the observations are 2, 4, 10, 12, 14, find the remaining two observations.

**30.** The mean and standard deviation of six observations are 8 and 4 respectively. If each observation is multiplied by 3, find the new mean and new standard deviation of the resulting observations.

**31.** Given that is the mean and σ^{2} is the variance of n observations x_{1}, x_{1}, ……, x_{n}. Prove that the mean and variance of the observations ax_{1}, ax_{2}, ax_{3}, ….., ax_{n} are and a^{2}σ^{2} respectively (a ≠ 0).

**32. **The mean and standard deviation of 20 observations are found to be 10 and 2 respectively. On rechecking, it was found that an observation 8 was incorrect. Calculate the correct mean and standard deviation in each of the following cases:

(i) if wrong item is omitted

(ii) if it is replaced by 12.

**33.** The mean and standard deviation of marks obtained by 50 students of a class in three subjects, Mathematics, Physics and Chemistry are given below:

Which of the three subjects shows the highest variability in marks and which shows the lowest?

**34. **The mean and standard deviation of a group of 100 observations were found to be 20 and 3 respectively. Later on it was found that three observations were incorrect, which were recorded as 21, 21 and 18. Find the mean and standard deviation if the incorrect observations are omitted.