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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

Copperhead and Tiger Snakes. S. Fearn et al. compare two types of snakes in the article 鈥淏ody Size and Trophic Divergence of Two Large Sympatric Elapic Snakes in Tasmania鈥� (Australian Journal of Zoology, Vol. 60, No. 3, pp. 159-165). Tiger snakes and lowland copperheads are both large snakes confined to the cooler parts of Tasmania. The weights of the male lowland copperhead in Tasmania have a mean of 812.07 g and a standard deviation of 330.24 g; the weights of the male tiger snake in Tasmania have a mean of 743.65 g and a standard deviation of 336.36 g.
a. Determine the z-scores for both a male lowland copperhead snake and a male tiger snake whose weights are 850 g.
b. Under what conditions would it be reasonable to use z-scores to compare the relative standings of the weights of the two snakes?
c. Assuming that a comparison using z-scores is legitimate, relative to the other snakes of its type, which snake is heavier?

Identify the two most commonly used measures of center for

quantitative data. Explain the relative advantages and disadvantages

of each.

How many standard deviations to either side of the mean must we go to ensure that for any data set, at least 99%of the observations lie within?

A quantitative data set of size 60has mean 100and standard deviation 16. At least how many observation lie between 68and132?

Fill in the following blanks.

(a) A standardized variable always has mean _____ and standard deviation _______ .

(b) The z-score corresponding to an observed value of a variable tells you ______ .

(c) A positive z-score indicates that the observation is ______ the mean, whereas a negative z-score indicates that the observation is _______ the mean.
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