Frequency Distributions

Q.

Calculate the mean and median for the following continuous frequency distribution.

$$\begin{array}{cc}\text{Class}& f_i\\ 0-10& 6\\ 10-20& 8\\ 20-30& 20\\ 30-40& 25\\ 40-50& 15\\ 50-60& 10\\ 60-70& 4\end{array}$$

1. 34.25, 32.4
2. 34.20, 34
3. 34.20, 32.1
4. 34, 32.1

Q. If the frequencies of first four numbers out of 1, 2, 4, 6, 8 are 2, 3, 3, 2 respectively, then the frequency of 8 if their A.M. is 5, is

1. 4
2. 5
3. 6
4. none of these

Q. If the frequencies of first four numbers out of 1, 2, 4, 6, 8 are 2, 3, 3, 2 respectively, then the frequency of 8 if their A.M. is 5, is

1. 4
2. 5
3. 6
4. none of these

Q. What is the median for the following set of data?
$$\begin{array}{cc}\text{Value}& \text{Frequency}\\ 0-5& 2\\ 5-10& 3\\ 10-15& 5\\ 15-20& 16\\ 20-25& 14\\ 25-30& 10\end{array}$$

1. 19.69
2. 15.67
3. 20.11
4. 11

Q. Consider the following frequency distribution:
$\begin{array}{cccccc}\text{Class:}& 0-6& 6-12& 12-18& 18-24& 24-30\\ \text{Frequency :}& a& b& 12& 9& 5\end{array}$
If mean $=\frac{309}{22}$ and median $=14,$ then the value $(a-b{)}^2$ is equal to

Q. ​​Calculate mean, variance, standard deviation for the following distribution
​Classes- 30-40 40-50 50-60 60-70 70-80 80-90 90-100
frequency 3 7 12 15 8 3 2

Q. The mean and median of a distribution are 22.5 and 20 respectively. The mode is approximately .

1. 20
2. 12
3. 15
4. 5

Q. If for some $x\in R$, the frequrency distribution of the marks obtained by $20$ students in a test is :

Marks	$2$	$3$	$5$	$7$
Frequency	$(x+1{)}^2$	$2x-5$	$x^2-3x$	$x$

then the mean of the marks is :

1. $2.5$
2. $3.2$
3. $3.0$
4. $2.8$