Chapter 3: Descriptive Measures

PGA Driving Distances. The PGA TOUR provides various statistics on performance of players in the Prof Association of America. For the week ending september $9,2013$, the year-to-date leader for longest average drive was B. his $773$drives, he averaged $298.5$yards. Assume Standard deviation of $19.7$yards.

a. Construct a graph
b. Apply Property $1$ of the empirical rule to make pertinent statements about the observations in the sample.
c. Repeat part (b) for Property $2$ of the empirical rule.
d. Repeat part (b) for Property $3$of the empirical rule.

Brain Weights. In $1905$, R. Pearl published the article "Biometrical Studies on Man. I. Variation and Correlation in Brain Weight" in which he studied the brain weights of Swedish males. The brain weights of a random sample of $225$Swedish men have a mean of $1.40kg$and standard deviation $0.11kg$.

a. Construct a graph
b. Apply Property $1$ of the empirical rule to make pertinent statements about the observations in the sample.
c. Repeat part (b) for Property $2$ of the empirical rule.
d. Repeat part (b) for Property $3$of the empirical rule.

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.

How many standard deviations to either side of the mean must we go to ensure that for any data set, at least $99\%$of the observations lie within?

How many standard deviations to either side of the mean must we go to ensure that for any data set, at least $95\%$of the observations lie within?

A data set consists of $2m^2-1$zeros, one $-m$, and one$m$.
a. Compute localid="1652585882368" $\tilde{x}$and$s$ for this data set.
b. How many standard deviations from the mean is the observationm ?
c. Assuming that $m\ge 4$, what percentage of the observations lie within three standard deviations to either side of the mean?

A data set contains$2m^2-1$ zeroes, one$-m$ and one $m$.

a. Compute$\hat{x}$ and$s$ for this data set.

b. How many standard deviations from the mean is the observation $m$?

c. Assuming that $m\ge 4$, what percentage of the observations lie within three standard deviations to either side of the mean?

A data set consists of $2m^2-1$zeroes, one $-m$and one $m$.

a. Compute $\hat{x}$and $s$for this data.

b. How many standard deviations from the mean is the observation m?

c. Assuming that $m\ge 4$, what percentage of the observations lie within three standard deviation to either side of the mean?

Identify by name three important groups of percentiles .

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