Two cricket teams kept records of the number of runs scored by their teams in 8 matches. The scores are shown in the following table.
| Team A | 150 | 220 | 77 | 30 | 298 | 118 | 160 | 57 |
| Team B | 166 | 142 | 170 | 93 | 111 | 130 | 148 | 86 |
- Find the mean and standard deviation of the scores for team A. [2]
- State with a reason which team has the more consistent scores. [2]
The mean and standard deviation for team B are 130.75 and 29.63 respectively.
Solution
(i) To find the mean for Team A:
Mean, \(\bar{x}_A = \frac{150 + 220 + 77 + 30 + 298 + 118 + 160 + 57}{8} = 139\).
To find the standard deviation for Team A:
\(First, calculate the variance:\)
Variance, \(s_A^2 = \frac{(150-139)^2 + (220-139)^2 + (77-139)^2 + (30-139)^2 + (298-139)^2 + (118-139)^2 + (160-139)^2 + (57-139)^2}{8}\).
\(s_A^2 = \frac{121 + 6561 + 3844 + 11881 + 25281 + 441 + 441 + 6724}{8} = 6901.25\).
Standard deviation, \(\sigma_A = \sqrt{6901.25} = 83.1\).
(ii) Team B has a smaller standard deviation (29.63) compared to Team A (83.1), indicating that Team B's scores are more consistent.
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