Standard Deviation about Mean

Q.

The standard deviation of the first n natural numbers is

1. none of these

2. $\frac{n+1}{2}$
   

3. $\sqrt{\frac{n(n+1)}{2}}$
   

4. $\sqrt{\frac{n^2-1}{12}}$
   

Q.

The mean of the numbers $a,b,8,5,10$ is $6$ and the variance is $6.80$. Then which one of the following gives possible values of $a$ and $b$?

1. $a=0,b=7$

2. $a=5,b=2$

3. $a=1,b=6$

4. $a=3,b=4$

Q. The standard deviation of 4, 7, 10, 13, 16, 19, 22 is

1. 2
2. 6
3. 8
4. 16

Q.

The table shows the daily changes in the barometric pressure (in inches of mercury) for four days.

(a) What is the mean change?

(b) The mean change for Monday through Friday is $-0.01$ inch. What is the change in the barometric pressure on Friday? Explain.

Day	Change in Pressure
Monday	$-0.05$
Tuesday	$0.09$
Wednesday	$-0.04$
Thursday	$-0.08$

Q.

In a series of $2n$ observations, half of them equal $a$ and remaining half equal $-a$. If the standard deviation of the observations is $2$, then $|a|$ equals.

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

2. $\sqrt{2}$

3. 2

4. $\frac{1}{n}$

Q. Mean and standard deviation of $100$ observations were found to be $40$ and $10$ respectively. If at the time of calculation two observations were wrongly taken as $30$ and $70$ in place of $3$ and $27$ respectively, find the correct S.D.

Q.

For observations $x_1,x_2,x_3,..........,x_n,$ if ${\sum }_{i=1}^n(x_i+1{)}^2=9n$ and ${\sum }_{i=1}^n(x_i-1{)}^2=5n.$, then standard deviation of the data is

1. $\sqrt{3}$
   

2. $\sqrt{5}$
   

3. $\sqrt{2}$
   

4. $\sqrt{10}$

Q. Find the mean deviations about the mean for the following data:

Marks obtained	10-20	20-30	30-40	40-50	50-60	60-70	70-80
Number of students	$2$	$3$	$8$	$14$	$8$	$3$	$2$