91Ó°ÊÓ

Regarding the five-number summary:
a. Identify its components.
b. How can it be employed to describe center and variation?
c. What graphical display is based on it?

What condition on a data set is required to apply the Empirical rule?

Each of the following smooth curves represents the shape of a data set. In each case, decide whether application of the empirical rule to the data set is appropriate. Explain your answers.

In this exercise, you will compare Chebyshev's rule and the empirical rule.

a. Compare the estimates given by the two rules for the percentage of observations that lie within two standard deviations to either side of the mean. Comment on the differences.

b. Compare the estimates given by the two rules for the percentage of observations that lie within three standard deviations to either side of the mean. Comment on the differences.

A quantitative data set has size $50$. At least how many observations lie within three standard deviation to either side of the mean$?$

The data set has mean $10$ and standard deviation$3$ . Fill in the following blanks:
a. Approximately $68\%$ of the observations lie between_ and _
b. Approximately$95\%$ of the observations lie between_ and _
c. Approximately$99.7\%$ of the observations lie between _and _

The data set has size$60$. Approximately how many observations lie within three standard deviations to either side of the mean?

Consider the following sample of exam scores, arranged in increasing order.

The sample mean and sample standard deviation of these exam scores are $85$and $16.1$, respectively.
a. Compare the percentage of the observations that actually lie within two standard deviations to either side of the mean with that given by Chebyshev's rule with$k=2$
b. Repeat part (a) with $k=3$
c. Interpret your results from parts (a) and (b).

Objects such as asteroids and comets that come into proximity with the Earth are called near-Earth objects (NEOs). The National Aeronautics and Space Administration (NASA) tracks and catalogues all NEOs that are at least $1$kilometer wide. Data on NEOs can be found on the NASA website; The following table gives the relative velocities in kilometers per second , arranged in increasing order, for the NEO close approaches to the earth during June $2013$.

The sample mean and sample standard deviation of these velocities are $11.9$and $6.5$ respectively.
a. Compare the percentage of the observations that actually lie within two standard deviations to either side of the mean with that given by Chebyshev's rule with$k=2$

b. Repeat part (a) with$k=3$

c. Interpret your results from parts (a) and (b).

Iron is essential to most life forms and to normal human physiology. It is an integral part of many proteins and enzymes that maintain good health. Recommendations for iron are provided in Dietary Reference Intakes, developed by the Institute of Medicine of the National Academy of Sciences, The recommended dietary allowance (RDA) of iron for adult females under the age of $51$is $18$milligrams (mg) per day. The iron intakes during a $24$-hour period for a random sample of$45$ adult females under the age of $51$have a mean of $14.7mg$and standard deviation of $3.1mg$.

a. Construct a graph .
b. Apply Chebyshev's rule with $k=2$ to make pertinent statements about the observations in the sample.
c. Repeat part (b) with $k=3$.