Standard Deviation about Mean for Continuous Frequency Distributions

Q. The variance of first $20$ natural numbers is

1. $133/4$
2. $399/4$
3. $133/2$
4. $279/12$

Q.

The binomial distribution for which mean = 6 and variance = 2, is

1. 
   

2. 
   

3. 
   

4. 
   

Q. If the sum and the product of mean and variance of a binomial distribution are $24$ and $128$ respectively, then the probability of one or two successes is:

Q.

What is the meaning of the term deviation?

Q.

The G.M of the numbers $3,3^2,3^3,.....3^n$ is

1. $3^{\frac{2}{n}}$

2. $3^{\frac{n+1}{2}}$

3. $3^{\frac{n}{2}}$

4. $3^{\frac{n-1}{2}}$

Q. In binomial probability distribution, mean is 3 and standard deviation $\frac{3}{2}$is

1. 
2. 
3. 
4. 

Q. In an experiment there are $20$ observation for which following results are given
$\sum x^2=8100,\sum x=214$
One observation that was $42$ was found to be wrong and it was replaced by the correct value $28$. Then the corrected standard deviation is

1. $15.8$
2. $16$
3. $12$
4. $21.35$

Q.

If $a$ be the arithmetic mean of $b$ and $c$ and $G_1,G_2$ be the two geometric means between them, then $G_1^3+G_2^3=$

1. $abc$
2. $2abc$
3. None of these
4. $3abc$

Q.

A box contains $15$ green and $10$ yellow balls. If $10$ balls are randomly drawn, one-by-one, with replacement, then the variance of the number of green balls drawn is

1. $\frac{12}{5}$

2. $\frac{6}{25}$

3. $6$

4. 4

Q.

Suppose, X has a binomial distribution B$(6,\frac{1}{2})$. Show that X=3 is the most likely outcome.

Q.

How do you find the arithmetic mean of grouped data $?$

Q. Two subsets A and B of a set ‘S’ consisting of ‘n’ elements are constructed randomly. The Probability that $A⊑B$ is equal to:

1. $\frac{1}{2^n}$
2. $(\frac{3}{4}{)}^n$
3. $\frac{2^n}{n!}$
4. $(\frac{2}{3}{)}^n$

Q. Mean and Standard Deviation of $100$ items are $50$ and $4$ respectively. The sum of all squares of the items is...

1. $266000$
2. $251600$
3. $261600$
4. $256100$

Q.

The mean deviation from the mean of the set of observations $-1,0,4$ is

1. $3$

2. $1$

3. $-2$

4. $2$

Q.

If the mean deviation of number $1,1+d,1+2d....,1+100d$from their mean is $255$, then $d$ is equal to

1. $10.0$

2. $20.0$

3. $10.1$

4. $20.2$

Q. Which of the following is not a measure of central location?

1. Mean
2. Median
3. Mode
4. Variance

Q.

Define the term variance.

Q. A sample space consists of integers $1,2,3,....100.$ The probability of choosing an integer $k$ is proportional to $\ln k$. The conditional probability of choosing the integer ${}^{\prime }{2}^{\prime }$, given that an even integer is chosen is

1. $\frac{\ln 2}{50\ln 2+\ln 50!}$
2. $\frac{\ln 2}{\ln 2+\ln 50!}$
3. $\frac{\ln 2}{50\ln 2+\ln 50}$
4. $\frac{\ln 2}{\ln 2+\ln 50}$

Q. The mean and variance of a random variable $X$ having a binomial distribution are $6$ and $3$ respectively. The probability of variable $X$ less than $2$ is

1. $\frac{13}{2048}$
2. $\frac{13}{4096}$
3. $\frac{25}{2048}$
4. $\frac{15}{4096}$

Q. The mean and the variance of a binomial distribution are 4 and 2 respectively. Then the probability of 2 successes is

1. $\frac{37}{256}$
2. $\frac{28}{256}$
3. $\frac{128}{256}$
4. $\frac{129}{256}$

Q.

In a meeting, $70\%$ of the members favour a certain proposal, $30\%$ being opposite. A member is selceted at random and let X=0, if he opposed and X=1, if he is in favour. Find E(X) and V(X)

Q. A die is thrown 6 times. If ‘getting an odd number’ is a success, then the probability of 4 successes is

1. $\frac{15}{64}$
2. $\frac{1}{4}$
3. $\frac{35}{64}$
4. $\frac{13}{64}$

Q. The coefficient of variance is $60$ and standard deviation is $24,$ then Arithmatic mean is

1. $40$
2. $\frac{7}{20}$
3. $\frac{20}{7}$
4. $\frac{1}{40}$

Q. In binomial distribution, the sum and the product of mean and the variance are $\frac{25}{3}$ and $\frac{50}{3}$ respectively. Determine the distribution.

Q. The mean and variance of a random variable $X$ having a binomial distribution are $6$ and $3$ respectively. Find the probability of variable $X$ less than $2$.

Q. Consider the following statements:
$1.$ Variance is unaffected by change of origin and change of scale.
$2.$ Coefficient of variance is independent of the unit of observations.
Which of the statements given above is/ are correct?

1. Both $1$ and $2$
2. $1$ only
3. Neither $1$ nor $2$
4. $2$ only

Q. Calculate the variance and standard deviation of the following continuous frequency distribution

Class interval	$30-40$	$40-50$	$50-60$	$60-70$	$70-80$	$80-90$	$90-100$
Frequency	$3$	$7$	$12$	$15$	$8$	$3$	$2$

Q. If the median of the data $6,7,x-2,x,18,21$ written in ascending order is $16$, then the variance of the data is

1. $30\frac{1}{5}$
2. $31\frac{1}{3}$
3. $32\frac{1}{2}$
4. $33\frac{1}{3}$

Q. The variance of the data $6,8,10,12,14,16,18,20,22,24$ is

1. $15$
2. $20$
3. $30$
4. $33$

Q. The variance of first $30$ natural numbers, is

1. $74.92$
2. $38.98$
3. $noneofthese$
4. $37.98$