Mean Deviation about Mean for Continuous Frequency Distributions

Q.

Calculate the mean deviation about the mean for the following frequency distribution :

$\begin{array}{cccccc}\text{Class Interval :}& 0-4& 4-8& 8-12& 12-16& 16-20\\ \text{Frequency :}& 4& 6& 8& 5& 2\end{array}$

Q. If n = 10800,
(a) Find total number of divisor of n.
(b) The number of even divisor.
(c) Find the number of divisor of the form 4m + 2.
(d) Find the number of divisor which are multiple of 15.

1. (a) 60
   (b) 48
   (c) 12
   (d) 30
2. (a) 60
   (b) 40
   (c) 15
   (d) 25
3. (a) 60
   (b) 44
   (c) 22
   (d) 38
4. (a) 60
   (b) 45
   (c) 22
   (d) 30

Q.

Calculate mean deviation from the median of the following data :

$\begin{array}{cccccc}\text{Class Interval :}& 0-6& 6-12& 12-18& 18-24& 24-30\\ \text{Frequency :}& 4& 5& 3& 6& 2\end{array}$

Q. If two ropes of equal length are divided into $18$ and $27$ pieces of equal size, then the length of the ropes can be

1. $54$
2. $72$
3. $108$
4. $144$

Q. Find the variance and standard deviation of the following data 5, 12, 3, 18, 6, 8, 2, 10

Q.

Find the mean of the following frequency distribution.

Class-interval	$15-25$	$25-35$	$35-45$	$45-55$	$55-65$
Frequency	$60$	$35$	$22$	$18$	$15$

Q.

The following table gives the literacy rate (in percentage) of $35$cities. Find the mean literacy rate.

Literacy rate (in $\%$)	$45-55$	$55-65$	$65-75$	$75-85$	$85-95$
Number of cities	$3$	$10$	$11$	$8$	$3$

Q. $7-3+\frac{9}{7}-\frac{27}{49}+....\infty$ equals

1. $49$
2. $10$
3. $4.9$
4. $\frac{49}{4}$

Q. Find the mean deviation about the mean for the data in

$x_i$	$5$	$10$	$15$	$20$	$25$
$f_i$	$7$	$4$	$6$	$3$	$5$

Q. A pack contains $n$ cards numbered from $1$ to $n$. Two consecutive numbered cards are removed from the pack and the sum of the numbers on the remaining cards is $1224$. If the smaller of the numbers on the removed cards is k, then $k-20$ is

Q. $g\left(x\right)=\frac{1}{x}$

Q. The function $f:N\to N$, where $N$ is the set of natural numbers, defined by $f\left(x\right)=7x+11$ is

1. injective
2. bijective
3. surjective
4. none of these

Q. If the variance of the following frequency distribution :
$\begin{array}{cccc}\text{Class}& 10-20& 20-30& 30-40\\ \text{Frequency}& 2& x& 2\end{array}$
is $50$, then $x$ is equal to