Illinois State University Mathematics Department


MAT 312: Probability and Statistics for Middle School Teachers

Dr. Roger Day (day@math.ilstu.edu)



Assignment #2: Possible Solutions


1. The required box plot is shown to the right. Because there are no data values beyond the fences (see [2cd] below), there are no data points represented using open or closed circles.

2. Required values:

a) 5-number summary: 0, 9.5, 19.5, 34, 63

b) lowspread: 19.5, midspread (IQR): 24.5, highspread: 43.5, range: 63

c) Here, 36.75 = (1.5)*IQR and 73.5 = (3.0)*IQR

d) From (2c), we note that there are no data values beyond the fences and therefore there are no outliers.

3. (histogram)

4.
mean: 21.875
median: 19.5
mode: 13

5. The data is anchored at the median (19.5 years) yet it ranges from 0 to 63 years. This indicates that the lower half of the data (the smallest 20 values in the data set) is between 0 and 20 years (lowspread of 19.5) and the upper half of the data (the largest 20 values in the data set) is between 20 and 63 years (highspread of 43.5). Thus, the upper half of the data is spread out more than twice as far as the lower half. In fact, the distance from the third quartile (34 years) to the maximum value (63 years) is larger than either the lowspread of the midspread. The distribution is positively skewed, indicated by the mean being larger than the median as well as by the majority of the data bunched in the lower portion of the distribution.