Question

The Department of Energy provides fuel economy ratings for all cars and light trucks sold in the United States. Offered are the estimated miles per gallon for city driving for the 186 cars classified as midsize in 2016, arranged in increasing order: 11 11 11 12 13 13 13 14 14 14 14 14 15 15 15 15 15 15 16 16 16 16 16 16 16 16 16 16 16 16 16 17 17 17 17 17 17 18 18 18 18 18 18 18 18 18 19 19 19 19 19 19 19 19 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 21 21 21 21 21 21 21 21 21 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 23 23 23 23 23 23 23 24 24 24 24 24 24 24 24 24 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 26 26 26 26 26 26 26 26 26 26 26 27 27 27 27 27 27 27 27 27 27 27 27 27 28 28 28 28 28 28 28 28 28 28 29 29 29 29 29 29 30 30 30 30 31 31 35 36 39 40 40 40 40 41 43 44 54 58

Give the five‑number summary of this distribution. (Round your entries to two decimal places.) Min= Q1= Median= Q3= Max= (b)

Select the correct boxplot representing these data. The box plot 2016 Midsize mpg values. The horizontal axis of the graph has no markings. The vertical axis of the graph shows mpg from 10 to 60 at succeeding intervals of 10. The five number summary, that is minimum, first quartile, Median, third quartile, and maximum, for the plot is depicted as 18.75, 32, 37.5, 44, and 56.5, respectively. The box plot 2016 Midsize mpg values. The horizontal axis of the graph has no markings. The vertical axis of the graph shows mpg from 10 to 60 at succeeding intervals of 10. The five number summary, that is minimum, first quartile, Median, third quartile, and maximum, for the plot is depicted as 11, 29.5, 41, 49, and 58, respectively. The box plot 2016 Midsize mpg values. The horizontal axis of the graph has no markings. The vertical axis of the graph shows mpg from 10 to 60 at succeeding intervals of 10. The five number summary, that is minimum, first quartile, Median, third quartile, and maximum, for the plot is depicted as 11, 18.75, 22, 27, and 58, respectively. The box plot 2016 Midsize mpg values. The horizontal axis of the graph has no markings. The vertical axis of the graph shows mpg from 10 to 60 at succeeding intervals of 10. The five number summary, that is minimum, first quartile, Median, third quartile, and maximum, for the plot is depicted as 13, 22, 29.5, 37, and 54, respectively.

What is the shape of the distribution shown by the boxplot?

Which features of the boxplot led you to this conclusion?

Are any observations unusually small or large?

The boxplot provided shows a symmetric distribution of mpg values. The boxplot provided shows right‑skew in the distribution of mpg values. There are high outliers from hybrid cars. The boxplot doesn't show any conclusive interpretation of the data. The boxplot provided shows left‑skew in the distribution of mpg values. There are low outliers from older cars with low mpg.

Answer #1

The five‑number summary of this distribution is

Min | 11 |

Q1 | 18.75 |

Median | 22 |

Q3 | 27 |

Max | 58 |

** The correct boxplot representing these
data:** The box plot 2016 Midsize mpg values. The horizontal
axis of the graph has no markings. The vertical axis of the graph
shows mpg from 10 to 60 at succeeding intervals of 10. The five
number summary, that is minimum, first quartile, Median, third
quartile, and maximum, for the plot is depicted as 11, 18.75, 22,
27, and 58, respectively.

**The shape of the distribution shown by the
boxplot:** The boxplot provided shows right‑skew in the
distribution of mpg values. There are high outliers from hybrid
cars.

**Unusually large observations:** **Outliers:
58 54 44 43 41 40 40 40 40**

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