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Chapter 2: Q 19. (page 107)

Tall or short? Mr. Walker measures the heights (in inches) of the students in one of his classes.

He uses a computer to calculate the following numerical summaries: Next, Mr. Walker has his entire class stand on their chairs, which are 18 inches off the ground. Then he measures the distance from the top of each student鈥檚 head to the floor.

(a) Find the mean and median of these measurements. Show your work.

(b) Find the standard deviation and IQR of these measurements. Show your work.

Short Answer

Expert verified

Part (a) The new mean is 87.188 and the new median is 87.5

Part (b) The deviations did not change and the IQR, Q1 and Q2, both increase by 18.

Step by step solution

01

Step 1. Given

02

Step 2. Concept

The formula used: Mean(new)=Sumofstudentheightsstandingonchairsnumberofstudents

03

Step 3. Calculation

The new mean and median both increase by 18 and can be found in the table below.

Mean(new)=Sumofstudentheightsstandingonchairs/numberofstudents=(heightoffirststudent+18)+...+(heightoflaststudent+18)/numberofstudents=Sumofstudentheightsstandingonfloor+18脳numberofstudents/numberofstudents=Mean(old)+18=69.188+18=87.188Median(new)=Median(old)+18=69.5+18=87.5

The new mean and median are 87.188 and87.5, respectively.

Therefore, the new mean is 87.188 and the new median is 87.5

04

Step 1. Explanation

While the mean grew by 18, the standard deviation increased by 18 as well, resulting in the deviations remaining unchanged. Q1 and Q3 both rise by 18 for the IQR, therefore their difference is the same as it was in the original data set.

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Most popular questions from this chapter

If30 is added to every observation in a data set, the only one of the following that is not changed is

(a) the mean. (d) the standard deviation.

(b) the 75th percentile. (e) the minimum.

(c) the median.

Speed limits According to the Los Angeles Times, speed limits on California highways are set at the 85th percentile of vehicle speeds on those stretches of road. Explain what that means to someone who knows little statistics.

R2.6 Horse pregnancies Bigger animals tend to carry their young longer before birth. The length of horse pregnancies from conception to birth varies according to a roughly Normal

distribution with a mean of 336 days and a standard deviation of 3 days. Use the 68-95-99.7 rule to answer the following questions.

(a) Almost all (99.7%)horse pregnancies fall in what range of lengths?

(b) What percent of horse pregnancies are longer than 339 days? Show your work.

Use Table A to 铿乶d the value zfrom the standard Normal distribution that satis铿乪s each of the following conditions. In each case, sketch a standard Normal curve with your value of zmarked on the axis. Use your calculator or the Normal Curve applet to check your answers.

Working backward

(a) The 10th percentile.

(b) 34% of all observations are greater thanz.

Use Table A to 铿乶d the proportion of observations from the standard Normal distribution that satis铿乪s each of the following statements. In each case, sketch a standard Normal curve and shade the area under the curve that is the answer to the question. Use your calculator or the Normal Curve applet to check your answers.

More Table A practice

(a) zis between 鈭�2.05and 0.78

(b) zis between 鈭�1.11and 鈭�0.32
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