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The following is the record of goals scored by team A in a football session.
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?
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?
Solution:
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Verified Answer
For Team A:
$\bar{x}=\frac{50}{25}=2$
S.D. $=\sqrt{\frac{\Sigma f_i x_i^2}{n}-\left(\frac{\Sigma f_i x_i}{n}\right)^2}=\sqrt{\frac{130}{25}-\left(\frac{50}{25}\right)^2}$
$=\sqrt{5.2-4}=\sqrt{1.2}=1.09$
For team $B, \bar{x}=2$, S.D. $=1.25$
Since their means are same, $\therefore \sigma_{\mathrm{A}}$ is less than that $\sigma_B$, therefore team $A$ is more consistent than team $B$.
$\bar{x}=\frac{50}{25}=2$
S.D. $=\sqrt{\frac{\Sigma f_i x_i^2}{n}-\left(\frac{\Sigma f_i x_i}{n}\right)^2}=\sqrt{\frac{130}{25}-\left(\frac{50}{25}\right)^2}$
$=\sqrt{5.2-4}=\sqrt{1.2}=1.09$
For team $B, \bar{x}=2$, S.D. $=1.25$
Since their means are same, $\therefore \sigma_{\mathrm{A}}$ is less than that $\sigma_B$, therefore team $A$ is more consistent than team $B$.
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