The scores on a 100-mark test of a sample of 80 students in a large school are given in the table.

SCORE: 59-63 63-67 67-71 71-75 75-79 79-83 83-87
# OF STUDENTS: 6 10 18 24 10 8 4

a) Find the mean and standard deviation of the scores of all students.

b) A bonus of 13 points is to be added to these scores. What is the new value of the mean and standard deviation?

(a) Mean =  72.1                        Standard deviation = 6.14

(b) New Mean =  85.1               New Standard deviation = 6.14

Step-by-step explanation:

We are given the scores on a 100-mark test of a sample of 80 students in a large school;

 Score      No. of students (f)      X       X*f            

59 - 63                6                       61       366          123.21                739.26

63 - 67                10                      65      650          50.41                 504.1

67 - 71                 18                      69      1242          9.61                   172.98

71 - 75                 24                     73       1752          0.81                   19.44

75 - 79                10                      77       770           24.01                 240.1

79 - 83                 8                       81       648           79.21                 633.68

83 - 87                4                       85      340         166.41               665.64    

                        ∑f = 80                      ∑X*f = 5768                     Total = 2975.2

(a) Mean of the above data, X bar = = = 72.1

Standard deviation, s = = = 6.14

Therefore, mean and standard deviation of the scores of all students are 72.1 and 6.14 respectively.

(b) Now, a bonus of 13 points is to be added to these scores.

So, Mean will also increases by 13 points and due to this;

New Mean = 72.1 + 13 = 85.1

Adding 13 points to each score will not affect standard deviation and due to which New standard deviation is same as before of 6.14.

correct answer:

b.(19,-2)

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