In a recent research article, the authors described the properties of the Friend

Question

In a recent research article, the authors described the properties of the Friendship Motivation Scale for Children (FMSC). Two interesting conclusions are that friends generally report similar levels of the FMSC and girls tend to score higher on the FMSC than boys. Boys in the 7th grade scored a mean of 9.32 with a standard deviation of 1.71, and girls in the 7th grade scored a mean of 10.04 with a standard deviation of 1.83.

Approximately 68% of 7th grade boys score between _____ and _____.

Approximately 95% of 7th grade boys score between _____ and _____.

Approximately 99.7% of 7th grade boys score between _____ and _____.

Explanation / Answer

a) By empirical rule , 68% of data lies between one standard deviation away from the mean

(9.32-1.71, 9.32+1.71)

(7.61, 11.03)

b)

By empirical rule , 95% of data lies between 2 standard deviation away from the mean

(9.32-2*1.71, 9.32+2*1.71)

(5.9, 12.74)

c) By empirical rule , 99.7% of data lies between 3 standard deviation away from the mean

(9.32-3*1.71, 9.32+3*1.71)

(4.19, 14.45)

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