Question

Six movies based on Marvel comic book characters for the U.S. box office as of fall 2017 are shown in the accompanying​ table, with domestic gross rounded to the nearest million. Complete parts​ (a) through​ (c) below.

Six movies based on Marvel comic book characters for the U.S. box office as of fall 2017 are shown in the accompanying​ table, with domestic gross rounded to the nearest million. Complete parts​ (a) through​ (c) below.

Movie	Domestic Gross ​($ millions)
The Avengers left parenthesis 2012 right parenthesisThe Avengers (2012)	677
Spiderman 2 left parenthesis 2004 right parenthesisSpiderman 2 (2004)	520
Avengers: Age of Ultron left parenthesis 2015 right parenthesisAvengers: Age of Ultron (2015)	471
Iron Man 3 left parenthesis 2013 right parenthesisIron Man 3 (2013)	434
Spiderman 3 left parenthesis 2007 right parenthesisSpiderman 3 (2007)	423
Captain America: Civil War left parenthesis 2016 right parenthesisCaptain America: Civil War (2016)	408

a. Sort the domestic gross income from smallest to largest. Find the median by averaging the two middle numbers. Interpret the median in context.

Put the domestic gross income​ ($ millions) in order from smallest to largest.

Find the median by averaging the two middle numbers. Interpret the median in context. Select the correct choice below and fill in the answer box within your choice.

​(Type an integer or a decimal. Do not​ round.)

A.The median is

nothing

million dollars. This means that about​ 25% of these 6 Marvel movies made more than this much money.

B.The median is

nothing

million dollars. This means that about​ 75% of these 6 Marvel movies made more than this much money.

C.The median is

nothing

million dollars. This means that none of these 6 Marvel movies made more than this much money.

D.The median is

nothing

million dollars. This means that about​ 50% of these 6 Marvel movies made more than this much money.

b. Using the sorted​ data, find Q1 and Q3. Then find the interquartile range and interpret it in context.

Find Q1.

Q1equals=_____million dollars ​(Type an integer or a decimal. Do not​ round.)

Find Q3.

Q3equals=_____million dollars ​(Type an integer or a decimal. Do not​ round.)

Find the interquartile range​ (IQR).

IQRequals=_____million dollars ​(Simplify your answer. Type an integer or a decimal. Do not​ round.)

Interpret the interquartile range in context. Choose the correct answer below.

A.

These 6 Marvel movies had domestic grosses that varied by as much as this value.

B.

This value is the difference between the maximum and minimum domestic grosses of these 6 Marvel.

C.

The middle​ 50% of these 6 Marvel movies had domestic grosses that varied by as much as this value

D.

This value is the mean domestic gross of these 6 Marvel movies.

c. Find the range of the data. Explain why the IQR is preferred over the range as a measure of variability.

Range=____million dollars ​(Simplify your answer. Type an integer or a decimal. Do not​ round.)

Why is the IQR preferred over the range as a measure of​ variability?

A.

The IQR depends on many observations and is therefore more reliable.

B.

The IQR depends on only two​ observations, the largest and the​ smallest, and is therefore more reliable.

C.

The IQR depends on only two​ observations, the mean and the​ median, and is therefore more reliable.

D.

The IQR depends on a single​ observation, and is therefore more reliable.

Answer 1

The domestic gross income when arranged from smallest to largest are:

408, 423, 434, 471, 520, 677

(a) Median = (434 + 471)/2 = 452.5

The median is 452.5 million dollars. This means that about 50% of these 6 Marvel movies made more than this much money

(b)

Q1 = 423

Q3 = 520

IQR = Q3 - Q1 = 97

Interquartile range -> The middle 50% of these 6 Marvel movies had domestic grosses that varied by as much as this value

(c)

Range = Maximum - Minimum = 677 - 408 = 169

IQR is preferred over the range as a measure of variability because

The IQR depends on many observations