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Chapter 3: Q. 3.149 (page 136)

Identify an advantage that the median and interquartile range have over the mean and standard deviation, respectively.

Short Answer

Expert verified

The advantage is that median and interquartile range are resistant to outliers.

Step by step solution

01

Given Information

We have to find out the advantage of median and interquartile range over the mean and standard deviation.

02

Explanation

Firstly, take an example that you have20students with their weight but one of the child weight is considered wrong it was taken 99but it was just 39then mean will have a huge difference but median will be same which shows that median is not changed by outliers.

The standard deviation is more changed by outliers as it is the square of differences between sample values and mean but the interquartile range is not changed because like median it does not take extreme values.

Hence, the advantage of the median and interquartile range over the mean and standard deviation is that they are not changed by outliers.

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Most popular questions from this chapter

Suppose you buy a new car whose advertised mileage is 25 miles per gallon (mpg). After driving your car for several months, you find that its mileage is 21.4mpg. You telephone the manufacturer and learn that the standard deviation of gas mileages for all cars of the model you bought is 1.15 mpg.

Part (a): Find the z-score for the gas mileage of your car, assuming the advertised claim is correct.

Part (b): Does it appear that your car is getting unusually low gas mileage?

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.

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

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.

The Beatles. In the article. "Length of The Beatles' Songs",(Chance Vol. 25. No. 1, pp. 30-33). T. Koyama discusses aspects and interpretations of the lengths of songs by The Beatles. Data on the length, in seconds, of 229 Beatles' songs are presented on the Weiss Stats site.
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