7 The mean and standard deviation of a group of observations were found to be and , respectively. Later on it was found that three observations were incorrect, which were recorded as and . Find the mean and standard deviation if the incorrect observations are omitted.
6. The mean and standard deviation of marks obtained by students of a class in three subjects, Mathematics, Physics and Chemistry are given below:
Subject 
Mathematics  Physics 
Chemistry 
Mean 

Standard deviation 
Which of the three subjects shows highest variability in marks and which shows the lowest?
5. The mean and standard deviation of observations are found to be and , respectively. On rechecking, it was found that an observation was incorrect. Calculate the correct mean and standard deviation in each of the following cases:
(ii) If it is replaced by
5. The mean and standard deviation of observations are found to be and , respectively. On rechecking, it was found that an observation was incorrect. Calculate the correct mean and standard deviation in each of the following cases:
(i) If wrong item is omitted.
4. Given that is the mean and is the variance of observations .Prove that the mean and variance of the observations , are and respectively, .
3. The mean and standard deviation of six observations are and , respectively. If each observation is multiplied by , find the new mean and new standard deviation of the resulting observations.
2. The mean and variance of observations are and , respectively. If five of the observations are . Find the remaining two observations.
1. The mean and variance of eight observations are and , respectively. If six of the observations are and , find the remaining two observations.
5. The sum and sum of squares corresponding to length (in cm) and weight (in gm) of 50 plant products are given below:
Which is more varying, the length or weight?
4. The following is the record of goals scored by team A in a football session:
No. of goals scored  0  1  2  3  4 
No. of matches  1  9  7  5  3 
For the team B, mean number of goals scored per match was 2 with a standard deviation goals. Find which team may be considered more consistent?
3. An analysis of monthly wages paid to workers in two firms A and B, belonging to the same industry, gives the following results:
Firm A 
Firm B 

No. of wage earners 

Mean of monthly wages 

Variance of the distribution of wages 
(ii) Which firm, A or B, shows greater variability in individual wages?
3. An analysis of monthly wages paid to workers in two firms A and B, belonging to the same industry, gives the following results:
Firm A 
Firm B 

No. of wage earners 

Mean of monthly wages 

Variance of the distribution of wages 
(i) Which firm A or B pays larger amount as monthly wages?
2 From the prices of shares X and Y below, find out which is more stable in value:
X  35  54  52  53  56  58  52  50  51  49 
Y  108  107  105  105  106  107  104  103  104  101 
1.From the data given below state which group is more variable, A or B?
Marks  1020  2030  3040  4050  5060  6070  7080 
Group A  9  17  32  33  40  10  9 
Group B  10  20  30  25  43  15  7 
10. The diameters of circles (in mm) drawn in a design are given below:
Diameters  3336  3740  4144  4548  4952 
No. of circles  15  17  21  22  25 
Calculate the standard deviation and mean diameter of the circles.
[ Hint First make the data continuous by making the classes as and then proceed.]
9. Find the mean, variance and standard deviation using shortcut method.
Height in cms  7075  7580  8085  8590  9095  95100  100105  105110  110115 
No. of students  3  4  7  7  15  9  6  6  3 
8. Find the mean and variance for the following frequency distributions.
Classes  010  1020  2030  3040  4050 
Frequencies  5  8  15  16  6 
7.Find the mean and variance for the following frequency distributions.
Classes  030  3060  6090  90120  120150  150180  180210 
Frequencies  2  3  5  10  3  5  2 
6 Find the mean and standard deviation using shortcut method.
60  61  62  63  64  65  66  67  68  
2  1  12  29  25  12  10  4  5 
5. Find the mean and variance for each of the data.
92  93  97  98  102  104  109  
3  2  3  2  6  3  3 