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Shoes How many pairs of shoes do students have? Do girls have more shoes than boys? Here
Chapter 2, Problem 1(choose chapter or problem)
How many pairs of shoes do students have? Do girls have more shoes than boys? Here are data from a random sample of 20 female and 20 male students at a large high school:
\(\begin{array}{lrrrrrrrrrr} \hline \text { Female: } & 50 & 26 & 26 & 31 & 57 & 19 & 24 & 22 & 23 & 38 \\ & 13 & 50 & 13 & 34 & 23 & 30 & 49 & 13 & 15 & 51 \\ \text { Male: } & 14 & 7 & 6 & 5 & 12 & 38 & 8 & 7 & 10 & 10 \\ & 10 & 11 & 4 & 5 & 22 & 7 & 5 & 10 & 35 & 7 \\ \hline \end{array}\)
(a) Find and interpret the percentile in the female distribution for the girl with 22 pairs of shoes.
(b) Find and interpret the percentile in the male distribution for the boy with 22 pairs of shoes.
(c) Who is more unusual: the girl with 22 pairs of shoes or the boy with 22 pairs of shoes? Explain.
Questions & Answers
QUESTION:
How many pairs of shoes do students have? Do girls have more shoes than boys? Here are data from a random sample of 20 female and 20 male students at a large high school:
\(\begin{array}{lrrrrrrrrrr} \hline \text { Female: } & 50 & 26 & 26 & 31 & 57 & 19 & 24 & 22 & 23 & 38 \\ & 13 & 50 & 13 & 34 & 23 & 30 & 49 & 13 & 15 & 51 \\ \text { Male: } & 14 & 7 & 6 & 5 & 12 & 38 & 8 & 7 & 10 & 10 \\ & 10 & 11 & 4 & 5 & 22 & 7 & 5 & 10 & 35 & 7 \\ \hline \end{array}\)
(a) Find and interpret the percentile in the female distribution for the girl with 22 pairs of shoes.
(b) Find and interpret the percentile in the male distribution for the boy with 22 pairs of shoes.
(c) Who is more unusual: the girl with 22 pairs of shoes or the boy with 22 pairs of shoes? Explain.
ANSWER:Step 1 of 3
The data from a random sample of 20 female and 20 male students at a large high school is given.
(a) Find and interpret the percentile in the female distribution for the girl with 22 pairs of shoes.
The observations which are less than 22 in the female distribution for the girl with 22 pairs of shoes are 13, 13, 13, 15, and 19.
So, the number of girls having less than 22 pairs of shoes is 5.
Thus, its percentile is \(\frac{5}{20}=0.25\).
Therefore, the percentile in the female distribution for the girl with 22 pairs of shoes is 25%.
Interpretation: The girl with 22 pairs of shoes is at the 25th percentile.