Question

Problem 2) Below is the list the highway gas mileages (in miles per gallon) of the randomly selected Honda car models. 22, 24, 26, 26, 28, 28, 29, 30, 30, 30, 31, 34, 34, 34, 34, 35, 36, 36, 41, 41 a) Construct a stem plot of the data set. Be sure to label the units. (4 pts.) b) What is the percentile of 34 miles per gallon

Answer 1

`\large \boxed{\text{b) 65th percentile}}`

Explanation:

a) Stem plot

A stem and leaf plot is a table that presents data values in a format similar to a histogram. Each data value is split into a "stem" (the first digit ) and a "leaf" (the last digit)

A stem and leaf plot for your data looks like this:

`\begin{array}l\textbf{Stem} & \textbf{Leaf} \\2 & 2\, 4\, 6\, 6\, 8\, 8\, 9 \\3 & 0\, 0\, 0\, 1\, 4\, 4\, 4\, 4\, 5\, 6\, 6 \\4 & 1\, 1 \\\end{array}`

b) Percentile

The percentile rank (PR) of a data value is the percentage of values that are equal to or less than that value.

The best formula for the percentile rank of a data value or score is

`PR = (L + 0.5S)/(N) * 100 \, \%`

where

L = number of values less than the score

S = number of values equal to the score

N = number of all values

For your data,

L = number of values less than 34 = 11

S = number of values equal to 34 = 4

N = number of values = 20

`\begin{array}{rcl}PR&= &(11 + 0.5*4)/(20) * 100 \, \%\\\\& = & (11 + 2)/(20) * 100 \, \%\\\\& = & (13)/(20) * 100 \, \%\\\\& = & 65 \, \%\\\end{array}\\\text{34 mi/gal is the $\large \boxed{\textbf{65th percentile}}$}`

Answer 2

a) Stem Leaf

2 | 2466889

3 | 00014444566

4 | 11

Where 3|4 means 34 and 2|2 means 22

b) For this case we want to find the percentile for the value 34 miles per gallon , and for this case we need to count how many number are below the number of 34, and if we see we got:

22, 24, 26, 26, 28, 28, 29, 30, 30, 30, 31, 34, 34, 34, 34

And we have 15 values below the number 34 and for the percentile we got:

`Percentile= (15)/(20) *100 = 75`

So would be the 75th percentile.

Explanation:

For this case we have the following data:

22, 24, 26, 26, 28, 28, 29, 30, 30, 30, 31, 34, 34, 34, 34, 35, 36, 36, 41, 41

Part a

We can create the stem plot like this:

Stem Leaf

2 | 2466889

3 | 00014444566

4 | 11

Where 3|4 means 34 and 2|2 means 22

Part b

For this case we want to find the percentile for the value 34 miles per gallon , and for this case we need to count how many number are below the number of 34, and if we see we got:

22, 24, 26, 26, 28, 28, 29, 30, 30, 30, 31, 34, 34, 34, 34

And we have 15 values below the number 34 and for the percentile we got:

`Percentile= (15)/(20) *100 = 75`

So would be the 75th percentile.