## Box and Whisker Plots Answers

1. a. b. From the box plots it can be seen that the grass grown in the sunny part has a much higher median length than grass grown in the shady part and three quarters of the sample grown in the sunny part was longer than the median length of grass grown in the shady part. It would appear, from these samples, that sunshine has a significant effect on the growth rate of grass.

2. a. The mean = 11.3 (to 1 decimal place). The standard deviation = 4.1 (to 1 decimal place).

b. c. The new mean = old mean + 4 = 15.3.

The standard deviation remains unchanged at 4.1

3. a. The median of test A is about 37 and the median of test B is about 59.

b. The marks in test A are skewed because the marks are much more spread between the median and the upper quartile than between the lower quartile and the median.

c. From the box plots it appears that the marks in test B are much more spread out than the marks in test A. The interquartile range is greater in test B as is the range.

 4 a. Fred Jon Median 90 87 Upper quartile 95 98 Lower quartile 83 80 Highest time 102 105 Lowest time 77 75 b. On average, Jon's times were better. Jon also had the fastest time of the season. However, Jon's times were more spread and Fred would apprear to be the more consistent runner.