Mean Deviation about Mean for Discrete Frequency Distributions

Q. The mean deviation about the mean for the following data :
$\begin{array}{cccccccc}{x}_i& 2& 3& 4& 5& 6& 7& 8\\ f_i& 5& 2& 3& 4& 5& 4& 2\end{array}$
is

1. $2.3$
2. $3.4$
3. $4$
4. $1.66$

Q. 5. x 9293 97 98 102 104 |109132

Q. 10 14 18 24 28 30f 2 47 12 8 434. x 6

Q. The mean deviation of the numbers 1, 2, 3, 4, 5 is

1. 0
2. 1.4
3. 1.2
4. 2

Q. 6.10 30 50 70 90x, f 4·24 28 16 8

Q. If the following frequency distribution
$\begin{array}{ccccccc}x& A& 2A& 3A& 4A& 5A& 6A\\ f& 2& 1& 1& 1& 1& 1\end{array}$
, where $A$ is a positive integer has a variance of $160$, then the value of $A$ is

Q.

Arjun and Karna had an archery competition where they had to shoot a target board with 7 concurrent circles dividing the board into 8 concurrent circular strips. Score for each outcome decreases by unity with centermost circle having score of 8. Dronacharya had difficulty in deciding who the winner was after the scores were recorded. Calculate the mean deviation about the score of innermost circle so as to decide who the winner is, assuming the winner is less deviated from the bull's eye.

$\begin{array}{ccccccccc}Points& 8& 7& 6& 5& 4& 3& 2& 1\\ Arjun\left(f_i\right)& 5& 7& 14& 23& 11& 10& 4& 3\\ Karna\left(f_i\right)& 5& 8& 11& 24& 14& 8& 5& 3\end{array}$

1. Arjun

2. Karna

3. Both of them

4. Insufficient data

Q. 55. x510 15 20 25133