Suppose the accompanying data on the top speed (in mph) for a sample of 24 roller coasters are taken
from a data base.
55 64 24 57 72 54 43 49 74 59 76 59
55 49 119 49 34 72 39 75 71 51 44 36
Construct a graphical display of the data distribution and then indicate what summary measures you would
use to describe center and variability.
The _____ should be used to describe the center and _______ should be used to
describe the variability.
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The median should be used to describe the center and interquartile range should be used to
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The graphical display of the data distribution can be constructed using a histogram or a box plot.
To construct a histogram, we would first create a frequency table to determine the number of roller coasters falling in each range of speeds. The histogram would then display the frequencies as bars on a graph, with the x-axis representing the speed ranges and the y-axis representing the frequency.
To construct a box plot, we would arrange the data in ascending order and determine quartiles (Q1, median, Q3). The box plot would display the minimum and maximum values as whiskers, the range between Q1 and Q3 as a box, and the median as a horizontal line within the box.
To describe the center, we would use the median. The median is a measure of central tendency that represents the middle value of the data. It is less affected by extreme values compared to the mean. In this case, the median would be the value that separates the lower 12 values from the upper 12 values when arranged in ascending order.
To describe the variability, we would use the range or the interquartile range (IQR). The range is the difference between the maximum and minimum values in the data set. It provides a measure of the spread of the data. The IQR is the range between the first quartile (Q1) and the third quartile (Q3). It represents the range of the middle 50% of the data and is less affected by extreme values compared to the range.
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