College

1.25 The following data set is related to that in Exercise 1.24. It gives the percentages of families in the upper income level for the same individual schools in the same order as in Exercise 1.24:

72.2, 31.9, 26.5, 29.1, 27.3, 20.4, 12.8, 25.1, 14.5, 19.2, 24.1, 8.6, 58.2, 22.3, 26.5, 55.1, 9.4, 13.9, 20.7, 17.9, 68.1, 8.5, 89.2, 55.4, 38.1, 54.2, 21.5, 26.2, 59.1, 43.3

Tasks:
(a) Calculate the sample mean.
(b) Calculate the sample median.
(c) Construct a relative frequency histogram of the data.
(d) Compute the 10% trimmed mean. Compare with the results in (a) and (b) and comment.

Answer :

Answer:

(a) To calculate the sample mean, sum all the data points and divide by the number of data points.

Sum of data points:

72.2 + 31.9 + 26.5 + 29.1 + 27.3 + 8.6 + 22.3 + 26.5 + 20.4 + 12.8 + 25.1 + 19.2 + 24.1 + 58.2 + 68.1 + 89.2 + 55.1 + 9.4 + 14.5 + 13.9 + 20.7 + 17.9 + 8.5 + 38.1 + 54.2 + 21.5 + 26.2 + 59.1 + 43.3 = 999.3

Sample mean:

Mean = Sum / Number of data points = 999.3 / 30 = 33.31

(b) To calculate the sample median, the data set must first be ordered from least to greatest. The middle value in the ordered list is the median.

Ordered data set: 8.5, 8.6, 9.4, 12.8, 13.9, 14.5, 17.9, 19.2, 20.4, 20.7, 21.5, 22.3, 24.1, 26.2, 26.5, 26.5, 27.3, 31.9, 38.1, 38.1, 43.3, 54.2, 55.1, 55.4, 58.2, 59.1, 68.1, 89.2

The median is the 15th value in the ordered list, which is 26.5.

(c) To construct a relative frequency histogram, we would divide each data point by the sum of all data points and then plot these values in a histogram. However, this is not possible to display in this text format.

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