Standard Deviation about Mean for Frequency Distributions

Q. The following is the record of goals scored by team A in a football session: No. of goals scored 0 1 2 3 4 No. of matches 1 9 7 5 3 For the team B, mean number of goals scored per match was 2 with a standard deviation 1.25 goals. Find which team may be considered more consistent?

Q. Find the mean and standard deviation using short-cut method.x60662 63 64 65 66 67 68f 21 12 29 252 10456.

Q.

Standard deviation about mean $\left(\overline{x}\right)$ for a given discrete frequency distribution $x_1,x_2,x_3,.....x_n$ with frequencies $f_1,f_2,f_3,...f_n$ is

1. 
   

2. 
   

3. 
   

4. 

Q.

Standard deviation about mean $\left(\overline{x}\right)$ for a given discrete frequency distribution $x_1,x_2,x_3,.....x_n$ with frequencies $f_1,f_2,f_3,...f_n$ is

1. $\sqrt{{\sum }_{i=1}^n\frac{(x_i-\overline{x}{)}^2}{n}}$
2. $\sqrt{\frac{{\sum }_{i=1}^{n}fi(x_i-\overline{x}{)}^2}{{\sum }_{i=1}^{n}fi}}$
3. $\frac{\sqrt{{\sum }_{i=1}^{n}fi(x_i-\overline{x}{)}^2}}{{\sum }_{i=1}^{n}fi}$
4. $\sqrt{\frac{{\sum }_{i=1}^{n}fi(x_i-\overline{x}{)}^2}{n}}$

Q. From the data given below state which group is more variable $A$ or $B$

Marks	10-20	20-30	30-40	40-50	50-60	60-70	70-80
Group A	9	17	32	33	40	10	9
Group B	10	20	30	25	43	15	7