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Howell Stuart
02/07/2022 · Senior High School
Consider the following set of ungrouped sample data. Answer parts A through D.
\( 4 \quad 3\quad 4 \quad 3 \quad 0 \quad 1\quad 5 \quad 5\)
(A) Find the mean and standard deviation of the ungrouped sample data.
\( \overline { x } = \square \) (Type an integer or a decimal.)
\( s = \square \) (Type an integer or decimal rounded to three decimal places as needed.)
(B) What proportion of the measurements lies within \( 1 \) standard deviation of the mean? Within \( 2 \) standard deviations? Within \( 3 \) standard deviations?
\(\square \% \) of the data values fall within \( 1 \) standard deviation of the mean.
\(\square \% \) of the data values fall within \( 2 \) standard deviations of the mean.
\(\square \% \) of the data values fall within \( 3 \) standard deviations of the mean.
(C) Based on your answers to part (B), would you conjecture that the histogram is approximately bell shaped? Explain.
A. Yes, because most of the data values fall near the mean with fewer data values farther from the mean.
B. Yes, because about the same number of data values fall near the mean as fall farther above and below the mean.
C. No, because most of the data values fall between \( 2 \) and \( 3 \) standard deviations from the mean.
D. No, because most of the data values fall farther than \( 3 \) standard deviations from the mean.
Expert-Verified Answer
Mean \( \overline { x } = \frac { \sum x } { n } \)
\( = \frac { 4 + 3 + 4 + 3 + 0 + 2 + 1 + 5 + 5 + 7 } { 10 } \)
\( = \frac { 34 } { 10 } \)
\( = 3.4\)
Sample Standard deviation \( S = \sqrt { \frac { \sum x ^ { 2 } - \frac { ( \sum x ) ^ { 2 } } { n } } { n - 1 } } \)
\( = \sqrt { \frac { 154 - \frac { ( 34 ) ^ { 2 } } { 10 } } { 9 } } \)
\( = \sqrt { \frac { 154 - 115.6 } { 9 } } \)
\( = \sqrt { \frac { 38.4 } { 9 } } \)
\( = \sqrt { 4.2667 } \)
\( = 2.0656\)
Home prices in Stanislaus county have a mean of \( \$ 266 K \) and a standard deviation of \( \$ 16 K \) . According to the empirical rule, what would be the upper and lower limit of the house prices for \( 99.7 \% \) of the houses?
Select one:
a. \( \$ 250 K \) and \( \$ 282 K \)
b. \( \$ 234 K \) and \( \$ 298 K \)
c. \( \$ 218 K \) and \( \$ 314 K\)
Health care issues are receiving much attention in both academic and political arenas. A sociologist recently conducted a survey of citizens over \( 60 \) years of age whose net worth is too high to qualify for Medicaid. The ages of \( 25 \) senior citizens were as follows:
60 65 71 76 87
61 66 73 76 89
62 68 74 81 90
63 69 74 81 95
64 69 76 83 96
1. Determine the median of the senior ages.
Health care issues are receiving much attention in both academic and political arenas. A sociologist recently conducted a survey of citizens over \( 60 \) years of age whose net worth is too high to qualify for Medicaid. The ages of \( 25 \) senior citizens were as follows:
\( 6065717687 - 6166737689 - 6268748190 - 6369748195 - 6469768396 \)
Determine the interquartile range of the ages of the senior citizens.
Health care issues are receiving much attention in both academic and political arenas. A sociologist recently conducted a survey of citizens over \( 60 \) years of age whose net worth is too high to qualify for Medicaid. The ages of \( 25 \) senior citizens were as follows:
\( 6065717687 - 6166737689 - 6268748190 - 6369748195 - 6469768396 \)
1. Determine the median of the senior ages.
Health care issues are receiving much attention in both academic and political arenas. A sociologist recently conducted a survey of citizens over \(60\) years of age whose net worth is too high to qualify for Medicaid. The ages of \(25\) senior citizens were as follows:
\(6065717687 - 6166737689 - 6268748190 - 6369748195 - 6469768396\)
Determine the interquartile range of the ages of the senior citizens.
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