NCERT Class 11-Math's: Exemplar Chapter –15 Statistics Part 9

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Question 21:

Following are the marks obtained, out of , by two students Ravi and Hashina in 10 tests.

Students Ravi and Hashina in 10 Tests
Students Ravi and Hashina in 10 tests

Ravi

25

50

45

30

70

42

36

48

35

60

Hashina

10

70

50

20

95

55

42

60

48

80

Who is more intelligent and who is more consistent?

Answer:

Given: the marks obtained, out of 100, by two students Ravi and Hashina in 10 tests

To find: who is more intelligent and who is more consistent

Case 1: For Ravi

The marks of Ravi being taken separately and finding other values can be tabulated as shown below,

The Marks of Ravi Being Taken Separately
The marks of Ravi being taken separately

Here we have assumed as mean.

Total there are marks of subjects.

Now we know standard deviation is given by,

Substituting the corresponding values, we get

And mean is

Hence the mean and standard deviation of the Ravi is 44.1 and 13 respectively.

Case 1: For Hashina

The marks of Hashina being taken separately and finding other values can be tabulated as shown below,

The Marks of Hashina Being Taken Separately
The marks of Hashina being taken separately

Here as so is mean.

Total there are marks of subjects.

Now we know standard deviation is given by,

Substituting the corresponding values, we get

Hence the mean and standard deviation of the Hashina is and respectively.

Now we will analyse them,

For Ravi,

For Hasina,

Now as of Hasina

Hence Ravi is more consistent.

Mean of HasinaMean of Ravi,

Hence Hasina is more intelligent.

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