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?

Asked by Abhisek | 11 months ago |  97

#### 1 Answer

##### Solution :-

$$\displaystyle\sum_{i=1}^{15} f_i x_i=\dfrac{50}{25}=2$$

Thus, the mean of both the teams is same

Variance = $$\dfrac{1}{N^2}[ N\displaystyle\sum f_i x_i^2-(\displaystyle\sum f_i x_i)^2]$$

$$\dfrac{1}{25^2}[(25\times 30)-2500]$$

$$\dfrac{750}{625}=1.2$$

Standard deviation σ = $$\sqrt{Variance}$$

$$\sqrt{1.2}$$  = 1.09

The standard deviation of team B is 1.25 goals. The average number of goals scored by both the teams is same i.e., 2. Therefore, the team with lower standard
deviation will be more consistent. Thus, team A is more consistent than team B.

Answered by Pragya Singh | 11 months ago

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