NCERT Class 11 Mathematics Solutions: Chapter 15 –Statics Miscellaneous Exercise Part 5

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In image standard deviation formulas are shon.

Standard Deviation Formulas

In image standard deviation formulas are shon.

1. The mean and standard deviation of marks obtained by students of a class in three subjects, Mathematics, Physics and Chemistry are given below:

Data of 50 students of a class
50 student of class in three subjects, mathematics, physics and chemistry are given.

Subject

Mathematics

Physics

Chemistry

Mean

Standard deviation

Which of the three subjects shows the highest variability in marks and which shows the lowest?

Answer:

Standard deviation of Mathematics

Standard deviation of Physics

Standard deviation of Chemistry

The coefficient of variation (C.V) is given by

The subject with greater C.V. is more variable than others.

So, the highest variability in marks is in Chemistry and the lowest variability in marks is in Mathematics.

2. The mean and standard deviation of a group of observations were found to be , respectively. Later on it was found that three observations were incorrect, which were recorded as . Find the mean and standard deviation if the incorrect observations are omitted.

Answer:

Number of observations

Incorrect mean

Incorrect standard deviation

Incorrect sum of observations

Correct sum of observations

Correct Mean

Standard deviation