17 Which score has a higher relative position a score of 111

17.

Which score has a higher relative position: a score of 111.3 on a test for which xbar = 130 and s = 18 , or a score of 301.2 on a test for which xbar = 335 and s = 27? (Note: \"xbar\" represents the mean value of the sample of tests collected.)

18.

Give an example of a situation where the median is likely a better average to use to describe the center location of quantitative data as compared to the mean.

19.

Explain what a standard deviation value measures in quantitative data?

20.

The graph at the right is a bar graph of the distribution of hours spent playing video games over the past week from a collection of randomly selected teenage males in the United States. Answer the following:

a.

How many teenage males were part of this study?

b.

Estimate the mean and the median length of time this group of selected teenage males spent gaming during the last week.

c.

Is the distribution symmetric, uniform, skewed left, skewed right, or none of these?

21.

The lengths of shoe laces in a newly operned package from various manufacturers are measured and recorded. The boxlpot to the right illustrates the summarized data collected from the various shoe laces.

a.

What is the interquartile range of the shoe lace lengths?

b.

Determine the median length of the shoe laces.

c.

Does the distribution of the lace lengths appear to be symmetric? Why or why not?

Solution

(17) Z-score= (X-mean)/s

For score 111.3,

Z=(111.3-130)/18 = -1.04

For score 301.2,

Z=(301.2-335)/27 = -1.25

Since Z=-1.25 is less than -1.04, score 111.3 has a higher relative position

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(18) The mean is the one to use with symmetrically distributed data; otherwise, use the median.

For example: income

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(19) The standard deviation are measures of the spread of the data which can be measured for quantitative data.

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(20) (a) 12+22+23+23+40+57+65+120+155+168+185+133+78+53+42=1176

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(b) mean =

(12*1+22*2+23*3+23*4+40*5+57*6+65*7+120*8+155*9+168*10+185*11+133*12+78*13+53*14+42*15)/1176

=9.579932

median=10

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(c)skewed left

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(21)(a) interquartile range= Q3-Q1 =65-45=20

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(b)median = 60

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(c) No, the distribution of the lace lengths do not appear to be symmetric because it shows skewed to the left.