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Refer to Exercise 79.

(a) Find the median by hand. Show your work. Interpret your result in context.

(b) Suppose Joey has an unexcused absence for the 15th quiz, and he receives a score of zero. Recalculate the mean and the median. What property of measures of center does this illustrate?

Short Answer

Expert verified

Part (a) The Median = 85

Part (b) Mean is 79.333 and the median is 84

Step by step solution

01

Part (a) Step 1: Given information

Given data:

86849175788074
87769682909893

The number of observations, n = 14

02

Part (a) Step 2: Concept

The formula used:M=N+12thobservation

03

Part (a) Step 3: Calculation

There is no center of observation for an even number of data variables. In the data, there is a center pair, 84and 86, with six observations before them and six observations after them in the order list. The average of these two observations is the median.

Median

M = 84+862

M = 85

Or Median can be calculated as follows:

Median

M = N+12thobservation

M = 14+12

M = 7.5thObservation

M = 7.5thObservation+8thobservation2

M = 84+862

M = 85

Interpretation: 50%of Joey's quiz grades are below85and 50%of Joey's quiz grades are above 85. Therefore, the median is 85

04

Part (b) Step 1: Calculation

Mean:

The values now include 0

86878476919675827890809874930

Mean = X

=Xi/n=sumofobservationsn=x1+x2+x3+....+xnn=86+87+84+76+91+96+75+82+78+90+80+98+74+9315=119015

Mean =79.33

Median:

Order all given data values:

07475767880828486879091939698

The median, or middle value of the sorted data collection, is 84because the number of data items is odd. It's worth noting that the mean fell from 85to 79.33, while the median fell from 85to 84. The outlier"0" had a much greater impact (reduction) on the mean than on the median, demonstrating that the median is resistant but the mean is not. As a result, the median is 84and the mean is 79.33The median is resistant to change, whereas the mean is not.

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