Standard deviation Practice Questions - NDA Mathematics Question Bank

Question 1 of 5 NDA MCQ

Consider the following for the next two (02)

items that follow:From 116Q to 117Q

The mean and standard deviation (SD) of marks obtained by 50 students of a class in 4 subjects are given below :

Which one of the following subjects shows highest variability of marks ?

Detailed Explanation

Question 2 of 5 NDA MCQ

Consider the following for the next two (02)

items that follow:

The mean and standard deviation (SD) of marks obtained by 50 students of a class in 4 subjects are given below :

What is the coefficient of variation of marks in
Mathematics ?

Detailed Explanation

Question 3 of 5 NDA MCQ

What is the standard deviation of the observations

−√6, −√5, −√4, −1, 1, √4, √5, √6 ?

Detailed Explanation

Solution

Option (b) is correct.

Explanation:

Given observations:

\[ x = \{-\sqrt{6}, -\sqrt{5}, -\sqrt{4}, -1, 1, \sqrt{4}, \sqrt{5}, \sqrt{6}\} \]

Calculate the mean (\(\mu\)):

\[ \mu = \frac{\sum x}{n} = \frac{-\sqrt{6} -\sqrt{5} -\sqrt{4} -1 + 1 +\sqrt{4} +\sqrt{5} +\sqrt{6}}{8} = 0 \]

Calculate the standard deviation (\(\sigma\)):

\[ \sigma = \sqrt{\frac{\sum (x - \mu)^2}{n}} = \sqrt{\frac{\sum x^2}{n}} \]

Compute \( \sum x^2 \):

\[ \sum x^2 = 6 + 5 + 4 + 1 + 1 + 4 + 5 + 6 = 32 \]

Thus, the standard deviation is:

\[ \sigma = \sqrt{\frac{32}{8}} = \sqrt{4} = 2 \]

📌 Hints / Properties Used:

Mean: \(\mu = \frac{\sum x}{n}\)
Variance: \( \sigma^2 = \frac{\sum (x - \mu)^2}{n}\)
Standard Deviation: \( \sigma = \sqrt{\sigma^2}\)

📊 Visual Diagram Suggestion:

A chart depicting the observations on a number line, highlighting their distance from the mean (0), and a bar graph showing squared differences from the mean.

📖 Factual Verification & Reference:

Verified against standard statistics textbooks.

Question 4 of 5 NDA MCQ

If the mean and the sum of squares of 10 observations are 40 and 16160 respectively, then what is the standard deviation ?

Detailed Explanation

Question 5 of 5 NDA MCQ

The standard deviation of 100 observations is 10. If 5 is added to each observation and then divided by 20, then what will be the new standard deviation?

Detailed Explanation

Standard deviation

Solution

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