Mean Deviation about Mean for Discrete Frequency Distributions

Q. There are $60$ students in a class. The following is the frequency distribution of the marks obtained by the students in a test

$\begin{array}{cc}\text{Marks}& \text{Frequency}\\ 0& x-2\\ 1& x\\ 2& x^2\\ 3& (x+1{)}^2\\ 4& 2x\\ 5& x+1\end{array}$

Where $x$ is positive integer. Then the variance of the marks is

1. $1.26$
2. $1.28$
3. $1.34$
4. $1.24$

Q.

Given are the observations of runs scored by batsmen between India - Sri Lanka combined. Find the mean deviation about mean for the scores of batsmen

$\begin{array}{ccccccc}Score& 0-10& 10-20& 20-30& 30-40& 40-50& 50-60\\ numberofBatsmen& 12& 18& 27& 20& 17& 6\end{array}$

1. 15

2. 99

3. 10

4. 50

Q.

Steven Gerard, arguably one of the most consistent and skilled player in English premier league was given monthly ratings by a Football website. The ratings are given on monthly basis. The following are the ratings for the past 40 months.

$\begin{array}{ccccccc}Rating& 6& 8& 8.5& 9& 7& 10\\ Numberofmonthswiththerating& 2& 8& 10& 7& 8& 5\end{array}$

Calculate how his rating is deviating from his average performance in terms of mean deviation about mean.

1. 0.825

2. 0.85

3. 0.9

4. 1