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A class of 63 children took an arithmetic test and obtained a mean score of 27.6 with a standard deviation of 7.1. Another set of 26 children, who had received less practice, had a mean score of 19.2 and a standard deviation of 6.2. When the two sets are combined, by how much do the mean and the standard deviation of the whole group differ from those of the original 63 children?
- 25.1, 7.8
- 2.3, 0.8
- 1.5, 0.9
- None of these
Correct answer: 2.3, 0.8
Solution
The mean of the combined groups is calculated by weighing the means of both sets based on their sizes, resulting in a new mean that differs from the original class. The standard deviation also changes due to the variation in scores between the two groups, leading to a slight increase in the overall standard deviation.
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