NCERT Grade 11-Statistics-Questions

NCERT Solutions for Class 11 Maths

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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.

5.     

6.     

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

7.     

8.     

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

9.     

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.  xi     6      10     14     18     24     28     30

fi     2       4        7      12      8       4       3

17.  xi     92      93     97     98     102     104     109

fi      3         2        3       2         6        3          3


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

xi     60      61     62     63     64     65     66     67     68

fi      2         1        12     29     25     12      10     4       5

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

19.   

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 σ2 is the variance of n observations x1, x1, ……, xn. Prove that the mean and variance of the observations ax1, ax2, ax3, ….., axn are  and a2σ2 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.

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