Question

Elementary Jon 25 34 Problem #2 (12 points) The following data set represents the miles per gallon rating for 30 ca 23 21 33 41 32 40 39 20 30 37 21 30 38 191919 26 28 29 35 35 36 32 38 38 (4 pts) a. Obtain the five-number summary for the data. (The five-number summary is: Minimum, Q1, Q2, Q3, and Maximum) (1 pt) b. Use the interquartile range (IQR) rule to identify any possible outlier (s) in the data. (4 pts) c. Construct a box-plot using the five number summary. Show outliers, if any. (1 pt) in the bottom 25% of the cars. d. Complete the following sentence: The miles per gallon rating is less than_ (2 pts) e. Circle the correct choice and fill in the blank: The (median/mean) better describes the center of this data set because the shape of this frequency distribution is

b d snd e only

Answer 1

Following is the output of descriptive statistics generated by excel:

Descriptive statistics х count 30 30.03 mean sample standard deviation sample variance 7.05 49.76 minimum 19 maximum 41 22 range 1st quartile 24.25 median 31.00 3rd quartile interquartile range 35.75 11.50 mode 19.00 low extremes low outliers high outliers high extremes BoxPlot 15 20 25 30 35 40 45

(b)

The interquartile range is

$IQR=Q_{3}-Q_{1}=35.75-24.25=11.5$

(d)

The miles per gallon rating is less than 24.25 in the bottom 25% of the cars.

(e)

Since box plot shows that distribution is approximately symmetric without any outlier so mean will be appropriate measure of central tendency.

Answers: mean and symmetric