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Why you use the standard deviation as a measure of variation. What is the reference point.

Complete the following statement: The descriptive measure is resistant if .......

Consider the data set 3,3,3,3,3,3.

Part (a) Guess the value of the sample standard deviation without calculating it. Explain your reasoning

Part (b) Use the defining formula to calculate the sample standard deviation.

Part (c) Complete the following statement and explain your reasoning. If all observation in a data set are equal, the sample standard deviation is

Part (d) Complete the following statement and explain your reasoning. If the sample standard deviation of a data set is 0 then...

Determine the age and sample standard deviation for each of the due sets. For the sample standard deviation round each answer to one more decimal place than that used for the observation.

Tornado Touchdowns. Each year, tornadoes that touch down are recorded by the Storm Prediction Center and published in Months Tomade Statistics. The following table gives the number of tornadoes that touched down in the United States during each month of one year [SOURCE: National Oceanic and Atmospheric Administration

In each Exercises 3.82-3.90, use the technology of your choice to determine and interpret the range and sample standard deviation for those data sets to which those concepts apply. If those concepts don't apply, explain why. Note: If an exercise contains more than one data set, perform the aforementioned tasks for each data set.

U.S. Hospitals. The American Hospital Association conducts annual surveys of hospitals in the United States and publishes its findings in AHA Hospital Statistics. Data on hospital type for U.S. registered hospitals can be found on the WeissStats site. For convenience, we use the following abbreviations:

• NPC: Nongovernment not-for-profit community hospitals
• IOC: Investor-owned (for-profit) community hospitals
• SLC: State and local government community hospitals
• FGH: Federal government hospitals
• NFP: Nonfederal psychiatric hospitals
• NLT: Nonfederal long-term-care hospitals
• HUI: Hospital units of institutions

In each Exercises 3.82-3.90, use the technology of your choice to determine and interpret the range and sample standard deviation for those data sets to which those concepts apply. If those concepts don't apply, explain why. Note: If an exercise contains more than one data set, perform the aforementioned tasks for each data set.

Ballot Preferences. In Issue 338 of the Amstat News, then president of the American Statistical Association, F. Scheuren reported the results of a survey on how members would prefer to receive ballots in annual elections. On the WeissStats site, you will find data for preference and highest degree obtained for the 566 respondents.

Weekly Salaries. In the following table, we repeat the salary data in Data Set II from Example 3.1.

(a) Use Definitions 3.4 and 3.6 on pages 99 and 108, respectively, to obtain the sample mean and sample standard deviation of this (ungrouped) data set.

(b) A frequency distribution for Data Set II, using single-value grouping, is presented in the first two columns of the following table. The third column of the table is for thexf- values, that is, classmark or midpoint (which here is the same as the class) times class frequency. Complete the missing entries in the table and then use the grouped-data formula to obtain the sample mean.

(c) Compare the answers that you obtained for the sample mean in parts (a) and (b). Explain why the grouped-data formula always yields the actual sample mean when the data are grouped by using single-value grouping. (Hint: What does xf represent for each class?)

(d) Construct a table similar to the one in part (b) but with columns for $x,f,x-\overline{x},{\left(x-\overline{x}\right)}^2,and{\left(x-\overline{x}\right)}^{2}f$.Use the table and the grouped-data formula to obtain the sample standard deviation.

(e) Compare your answers for the sample standard deviation in parts (a) and (d). Explain why the grouped-data formula always yields the actual sample standard deviation when the data are grouped by using single-value grouping.

Specify the mathematical symbol used for each of the following descriptive measures. a. Sample mean b. Sample standard deviation c. Population mean d. Population standard deviation.

Data Set A has more variation than Data Set B. Decide which of the following statements are necessarily true.

a. Data Set A has a larger mean than Data Set B.

b. Data Set A has a larger standard deviation than Data Set B.

What does Chebyshev's rule say about the percentage of observations in any data set that lie within

(a) six standard deviations to either side of the mean?

(b) 1.5 standard deviations to either side of the mean?