NCERT Class 11-Math՚s: Exemplar Chapter – 15 Statistics Part 9 (For CBSE, ICSE, IAS, NET, NRA 2023)

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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
Ravi25504530704236483560
Hashina10705020955542604880

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

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

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 Hasina Mean of Ravi,

Hence Hasina is more intelligent.