Variance and Standard Deviation

Q.

What is the difference between mean and standard deviation?

Q.

Can the standard deviation ever be negative?

Q.

If the value observed are $1,2,3,...,n$ each with frequency $1$ and $n$ is even, then the mean deviation from mean equals to

1. $n$

2. $\frac{n}{2}$

3. $\frac{n}{4}$

4. None of these

Q.

Indicate the most appropriate alternative from the multiple choices provided against each question.

(i) The most suitable average for qualitative measurement is

(a) Arithmetic mean (b) Median

(c) Mode (d) Geometric mean

(e) None of these

(ii) Which average is affected most by the presence of extreme items?

(a) Median (b) Mode

(c) Arithmetic mean (d) Geometric mean

(e) Harmonic mean

(iii) The algebraic sum of deviation of a set of n values from AM is

(a) n (b) 0

(c) 1 (d) None of these

Q.

Can You Have A Negative Standard Deviation

Q. The first of two samples has $100$ items with mean $15$ and S.D. $3$. If the whole group has $250$ items with mean $15.6$ and $s.d=\sqrt{13.44}$, find the standard deviation of the second group.

1. $5$
2. $4$
3. $3.52$
4. $6$

Q. Which of the following is true about standard deviation?

1. It is a measure of spread of data about the mean.
2. It is the cube root of sum of squared deviation from the mean divided by the number of observations.
3. Both are correct
4. None is correct

Q. Mean and standard deviation of runs scored by a cricket player are $80$ and $4$ respectively. Find the coefficient of variation.

Q. The S.D. of the numbers 31, 32, 33, .... 47 is

1. $2\sqrt{6}$
2. $\sqrt{\frac{{47}^2-1}{12}}$
3. $4\sqrt{3}$
4. None of these

Q. Which of the following is used to compare the variation or dispersion in two or more sets of data even though they are measured in different units?

1. Range
2. Variance
3. Coefficient of variation
4. None of these