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Chapter 2: Problem 86

Indicate whether the five number summary corresponds most likely to a distribution that is skewed to the left, skewed to the right, or symmetric. (22.4,30.1,36.3,42.5,50.7)

Short Answer

Expert verified
The five number summary corresponds most likely to a distribution that is symmetric.

Step by step solution

01

Identify the five number summary

The given five number summary includes the following values: minimum = 22.4, Q1 = 30.1, median = 36.3, Q3 = 42.5, and maximum = 50.7.
02

Compute distances

Next compute the distances between the median and Q1 as well as the median and Q3. From Q1 to the median is \(36.3 - 30.1 = 6.2\) and from the median to Q3 is \(42.5 - 36.3 = 6.2\).
03

Compare distances

Since the distances from Q1 to the median and from the median to Q3 are equal, it suggests that the data is symmetrically distributed. The median is in the middle of Q1 and Q3 and not leaning towards any side.

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Most popular questions from this chapter

A survey conducted in May 2010 asked 1917 cell phone users to estimate, on average, the number of text messages sent and received per day. (a) Do you expect the distribution of number of text messages per day to be symmetric, skewed to the right, or skewed to the left? (b) Two measures of center for this distribution are 10 messages and 39.1 messages. \({ }^{32}\) Which is most likely to be the mean and which is most likely to be the median? Explain your reasoning.

Presidential Elections In Example 2.43 on page \(123,\) we use the approval rating of a president running for re-election to predict the margin of victory or defeat in the election. We saw that the least squares line is \(\widehat{\text { Margin }}=-36.5+0.836(\) Approval \()\). Interpret the slope and the intercept of the line in context.

Calculate the mean and the median for the numbers \(1, \quad 1, \quad 1, \quad 1, \quad 1, \quad 1, \quad 2, \quad 5,7, \quad 12\) Which do you think is a better measure of center for this set of values? Why? (There is no right answer, but think about which you would use.)

The survey students consisted of 169 females and 193 males. Find \(\hat{p},\) the proportion who are female.

Each describe a sample. The information given includes the five number summary, the sample size, and the largest and smallest data values in the tails of the distribution. In each case: (a) Clearly identify any outliers. (b) Draw a boxplot. Five number summary: (15,42,52,56,71)\(;\) \(n=120\) Tails: \(15,20,28,30,31, \ldots, 64,65,65,66,71\)
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