Standard Deviation

Q.

All the students of a class performed poorly in mathematics. The teacher decided to give grace marks of $10$ to each of the students. Which of the following statistical measures will not change even after the grace marks were given?

1. Mean

2. Median

3. Mode

4. Variance

Q. The standard deviation of a given set of data is 20. If each of the value in the data is increased by 3, then the new standard deviation is .

1. 17
2. $23$
3. 20
4. $20+\sqrt{3}$

Q. The Standard Deviation of a sample of size 10 is 11. If the value of each sampled item is reduced by 2, the new Standard deviation will be

1. 9
2. 11
3. 13
4. 22

Q.

The standard deviation of 25 numbers is 40. If each of the numbers is increased by 5, then the new standard deviation will be

1. 40

2. 45

3. none of these

4. $40+\frac{21}{25}$

Q. Compute the missing frequencies ${}^{\prime }{f}_1^{\prime }$ and ${}^{\prime }{f}_2^{\prime }$ in the following data, if the mean is $166\frac{9}{26}$ and the sum of the observation is 52.

Classes	Frequency
140-150	5
150-160	$f_1$
160-170	20
170-180	$f_2$
180-190	6
190-200	2
Total	52

1. $f_1=7,f_2=3$
2. $f_1=10,f_2=6$
   
3. $f_1=9,f_2=8$
4. None of these

Q. The standard deviation of a set of scores is $1.6$. The variance of these scores is

1. $0.4$
2. $0.04$
3. $2.56$
4. $1.96$

Q. In a set of $2n$ observations, half of them are equal to '$\alpha$' and the remaining half are equal to '$-\alpha$'. If the standard deviation of all the observations is $2$, then the value of $|\alpha |$ is equal to

1. $2$
2. $\sqrt{2}$
3. $2\sqrt{2}$
4. $4$

Q. If we add the square of the digit in the tens place of a positive two digit number to the product of the digits of that number, we shall get $52$ and if we add the square of the digit in the units place to the same product of the digits, we shall get $117$. Find the two-digit number.