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Chapter 3: Q. 3.152 (page 136)

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

Short Answer

Expert verified

All the properties of symmetric, left-skewed and right-skewed distributions depends upon the position of median.

Step by step solution

01

Given Information

We have to find out the pertinent properties of boxplots for symmetric, left-skewed and right-skewed distributions.

02

Explanation

The properties of boxplots depends upon the position as following

a) When median is in the middle of boxplot and whisker is same on the both side then it is called symmetric distributions.

b) When the median is closed to the bottom of the box and whisker is shorter on lower end of the box then it is called right-skewed distributions.

c) When the median is closed to the top of the box and whisker is shorter on upper end of the box then it is called left-skewed distributions.

Hence, these are the properties of boxplots distributions.

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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.

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
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A company produces cans of stewed tomatoes with an advertised weight of 14oz. The standard deviation of the weights is known to be 0.4oz. A quality - control engineer selects a can of stewed tomatoes at random and finds its net weight to be 17.28oz.

Part (a): Estimate the relative standing of that can of stewed tomatoes, assuming the true mean weight is 14oz. Use the z-score and Chebyshev's rule.

Part (b): Does the quality - control engineer have reason to suspect that the true mean weight of all cans of stewed tomatoes being produced is not 14oz? Explain your answer.

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(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.

Identify a use of lower and upper limits.

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