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Chapter 3: Q.3.73. (page 93)

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

Short Answer

Expert verified

Range of the data=202tanadoes

Standard deviation of the data

Step by step solution

01

Step 1. Given information.  

We have given data ;

01

Step 1. Given information. 

We have given data ;3,2,47,118,204,97,68,86,62,57,98,99

02

Step 2. To find range of the data.

Range=Max.value-Min.value=204-2=202tamadoes

03

Step 3. To find mean of the data.

Mean=SumoftheobservationNumberofobservation=(2+3+47+118+204+97+68+86+62+57+98+99)12=94112=78.41667=78.4

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Most popular questions from this chapter

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.

Find the

a. Mean b. median c. mode

For the mean and the median, round each answer to one more decimal place than that used for the observations.

Daily Motorcycle Accidents. The Scottish Executive, Analy. tical Services Division Transport Statistics, compiles data on motor cycle accidents. During one year, the numbers of motorcycle accidents in Scotland were tabulated by day of the week for built-up roads and non-built-up roads and resulted in the following data .

a. Find the mean and median of the number of accidents for built-up roads.

b. Find the mean and median of the number of accidents for non built-up roads.
c. If you had a list of only the day of the week for each accident, what day would be the modal day for each type of road?
d. What might explain the difference in the modal days for the two types of roads?

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

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-x,x-x2,andx-x2f.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.

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 1kilometer 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 11.9and 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 withk=2

b. Repeat part (a) withk=3

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