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The cheetah (Acinonyx jubatus) is the fastest land mammal and is highly specialized to run down prey. The cheetah often exceeds speeds of $60$miles per hour (mph) and. according to the online document "Cheetah Conservation in Southern Africa" by J. Urbaniak, the cheetah is capable of speeds up to $72mph$The following table gives the top speeds, in miles per hour, arranged in increasing order, for a sample of $35$cheetahs.

The sample mean and sample standard deviation of these speeds are $59.53mph$and $4.27mph$, respectively. A histogram of the speeds is bell shaped.
a. Is it reasonable to apply the empirical rule to estimate the percentages of observations that lie within one, two, and three standard deviations to either side of the mean?
b. Use the empirical rule to estimate the percentages of observations that lie within one, two, and three standard deviations to either side of the mean.
c. Use the data to obtain the exact percentages of observations that lie within one, two, and three standard deviations to either side of the mean.
d. Compare your answers in parts (b) and (c).

What does Chebyshev's rule say about the percentage of observations that lie within one standard deviation to either side of the mean? Discuss your answer.

Identify an advantage that the median and interquartile range have over the mean and standard deviation, respectively.

Explain why minimum and maximum observations are added to the three quartiles to describe better the variation in a data set.

State pertinent properties of boxplots for symmetric, left-skewed and right-skewed distributions.

Regarding the interquartile range,

(a) What type of descriptive nature is it?

(b) What does it measure?

Identify a use of lower and upper limits.

Which measure of variation is preferred when

(a) the mean is used as a measure of center?

(b) the median is used as a measure of center?

Fill in the blanks: Roughly, when arranged in increasing order, the uppermost $25\%$of the dataset are greater than or equal to _______ .

We have provided simple data sets for you to practice finding the descriptive measures discussed in this section. For each data set.

Obtain the quartiles, determine the inter quartile range, find the five-number summary.

$1,2,3,4,1,2,3,4$