NCERT Class 11 Mathematics Solutions: Chapter 15 –Statics Miscellaneous Exercise Part 5
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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:
| Subject | Mathematics | Physics | Chemistry |
| Mean |
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|
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| Standard deviation |
|
|
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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