Twenty students sat a mathematics test and obtained the following scores (in marks): 45, 52, 58, 60, 62, 65, 68, 70, 71, 73, 74, 76, 78, 80, 82, 85, 88, 90, 92, 95.

(a) Calculate the arithmetic mean $ \bar{x} $ of the original scores.

(b) Remove the two lowest and two highest scores and calculate the new mean $ \bar{x}_{\text{trim}} $ of the remaining data.

(c) Based on the original data, state whether the distribution is positively skewed, negatively skewed, or symmetric.

Question

Twenty students sat a mathematics test and obtained the following scores (in marks): 45, 52, 58, 60, 62, 65, 68, 70, 71, 73, 74, 76, 78, 80, 82, 85, 88, 90, 92, 95.

(a) Calculate the arithmetic mean $ \bar{x} $ of the original scores.

(b) Remove the two lowest and two highest scores and calculate the new mean $ \bar{x}_{\text{trim}} $ of the remaining data.

(c) Based on the original data, state whether the distribution is positively skewed, negatively skewed, or symmetric.

Accepted Answer

Mean = 73.2; Trimmed mean = 73.75; Distribution is negatively skewed

Neco 2017 Data Processing Question 11

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