# Compute Standard Deviation from a frequency table

X P(X=x)

(5 @ .12)

(6 @ .24)

(8 @ .44)

(10 @ .20)

What is the standard deviation of X?

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#### Solution Preview

So, standard deviation is computed as follows...

sqrt[E(x^2)-(Ex)^2]

So to find E(x) (the mean) we ...

#### Solution Summary

A step-by-step solution shows the student how to calculate the standard deviation given a probability distribution.

Frequency Distribution Table, Stem and Leaf Plot, Histogram, Z-Score and other Problems

[Please see attachment for data and charts]

1. Identify each number as either continuous or discrete.

a. The average speed of cars passing a speed trap on the Maine Turnpike between 3 PM and 6 PM on a given Monday.

b. A census taker wants to know the number of Maine families with preteens.

c. The temperature of the ocean at various depths.

2. For each of the following variables, indicate whether it is qualitative or quantitative.

a. The admitting diagnosis of patients admitted to a mental health clinic.

b. The weights of babies born in a hospital during a year.

c. The class rank of high school seniors at the local high school.

d. The religion of the sample subjects.

3. Identify each study as either experimental or observational.

a. A sample of fish is taken from the Androscoggin River, in Maine, to measure the level of mercury in the fish.

b. A research scientist gives a weight loss drug to a group of 500 patients and a placebo to another 500 patients to determine if the weight loss drug has an effect on the patients.

4. In response to a poll on a Dateline NBC program about wildlife conservation, 1276 of 1450 callers said they would be willing to spend more money on imported fossil fuels in order to eliminate the possibility of oil drilling in national parks set aside as wildlife preserves. NBC followed with the announcement that 88% of Americans are willing to spend money to protect wildlife preserves. Do you think that the group of people who responded is likely to be representative of all Americans? Explain your answer.

5. Construct a frequency table with 4 classes for the following data on the charge for monthly long distance phone bills for the last year: $17.06, $20.96, $25.97, $26.41, $22.02, $27.34, $18.67, $24.88, $24.07, $25.35, $23.39, $20.60.

6. Find the original data from the stem-and-leaf plot.

7. The winners of the NCAA wrestling championships for the years 1968-1997 are

given in the table below.

a. Compute relative frequencies for each class and fill in the appropriate column

of the table. Round all relative frequencies to 3 decimal places.

b. Draw the relative frequency histogram for the above table.

8. Consider the following relative frequency histogram displaying the number of cars

sold per week last year for a given sales rep, Ronnie, at Emerson Toyota.

Given that there are 52 weeks in a year, approximately how many times did Ronnie

sell 2 cars per week? Round your answer to the nearest whole week.

9. The average retail price for bananas in 1994 was 46.0 cents per pound, as reported

by the U.S. Department of Agriculture. A recent random sample of 8 supermarkets

gave the following prices for bananas in cents per pound.

a. Find the mean price for bananas per pound. Round to 3 decimal places.

b. Find the median price for bananas per pound.

c. Find the mode price for bananas per pound.

10. The number of absences for five children in a local kindergarten class is as follows.

a. Complete the table and use the computing formula

to find the standard deviation for the number of absences. Round to 3 decimal

places. Note: if you would prefer to use the other formula for standard

deviation then adjust the table accordingly.

b. What is the range for the number of absences?

c. Which appears to be a better measure of variation for this data set: range or

standard deviation?

d. What is the variance?

11. True or False.

For the data set {2,3,4,3,6,75}, the median is a better measure of

center than the mean. Explain.

12. Suppose that the mean score on this test is 75.6 with a standard deviation of 7.8.

Suppose also that the scores follow a bell-shaped distribution.

a. Convert a score of 80 to a z-score. Round your answer to 2 decimal places.

b. How many standard deviations is a score of 80 from the mean?