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Chapter 2: Q 31. (page 108)

Mean and median The figure below displays two density curves, each with three points marked. At which of these points on each curve do the mean and

the median fall?

Short Answer

Expert verified

Part (a) Mean is C, the median is B

Part (b) Mean is B, median is also B

Step by step solution

01

Part (a) Step 1. Given

02

Part (a) Step 2. Concept

A density curve is the graph of a continuous distribution.

03

Part (a) Step 3. Explanation

The median is B, and the mean is C. (the right skew pulls the mean to the right).

Because the mean is more influenced by extreme values than the median, the mean must lie to the right of the median.

Because they cannot lie on the peak of a skewed distribution, the median and mean do not lie at A. (tail of extreme values causes both to lie more to the right). As a result, we know:

B= Median

C= Mean

Therefore, the Mean is C, the median is B.

04

Part (b) Step 1. Given

05

Part (b) Step 2. Explanation 

Because the distribution is symmetric about its middle point B (the graph is the mirror image to the left of the middle as it is to the right), the mean is located here: 渭=B

Because the area beneath the graph is 0.50 on each side of the mean.

MEDIAN = B

B is the mean, and B is the median (this distribution is symmetric).

Therefore, Mean is B, median is also B.

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Most popular questions from this chapter

Measure up Clarence measures the diameter of each tennis ball in a bag with a standard ruler. Unfortunately, he uses the ruler incorrectly so that each of his

measurements is 0.2inches too large. Clarence鈥檚 data had a mean of 3.2inches and a standard deviation of 0.1 inches. Find the mean and standard deviation of the corrected measurements in centimeters (recall that 1 inch = 2.54 cm).

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T2.3. Rainwater was collected in water collectors at 30different sites near an industrial complex, and the amount of acidity (pH level) was measured. The mean and standard deviation of the values are 4.60and 1.10, respectively. When the pH meter was recalibrated back at the laboratory, it was found to be in error. The error can be corrected by adding 0.1pHunits to all of the values and then multiplying the result by 1.2. The mean and standard deviation of the corrected pH measurements are

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The distribution of heights of adult American men is approximately Normal with mean of 69inches and a standard deviation of 2.5inches. Draw a Normal curve on which this mean and standard deviation are correctly located. (Hint: Draw the curve first, locate the points where the curvature changes, and then mark the horizontal axis.

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