Chapter 2.1, Problem 19E

Smartphone sales: The following frequency distribution presents the number of smartphones (in millions) shipped in each quarter of each year from 2012 through 2015.

1. Construct a frequency bar graph.
2. Construct a relative frequency distribution.
3. Construct a relative frequency bar graph.
4. True or false: In each year, the quarter with the largest sales was October to December.

To determine

To construct: A frequency bar graph.

Explanation of Solution

Given information: The following frequency distribution presents the number of smartphones (in millions)shipped in each quarter of each year from 2012 through 2015.

Quarter	Number sold (in millions)
Jan.-Mar. 2012	152.7
Apr.-Jun. 2012	156.2
Jul.-Sep. 2012	179.7
Oct.-Dec. 2012	227.8
Jan.-Mar. 2013	222.6
Apr.-Jun. 2013	253.3
Jul.-Sep. 2013	276.6
Oct.-Dec. 2013	292.7
Jan.-Mar. 2014	288.4
Apr.-Jun. 2014	302.1
Jul.-Sep. 2014	332.6
Oct.-Dec. 2014	377.8
Jan.-Mar. 2015	334.4
Apr.-Jun. 2015	337.2
Jul.-Sep. 2015	355.2
Oct.-Dec. 2015	399.5

Solution:

From the given table, the frequency bar graph is given by

  

To determine

To construct: The relative frequency distribution.

Explanation of Solution

Given information:The following frequency distribution presents the number of smartphones (in millions) shipped in each quarter of each year from 2012 through 2015.

Quarter	Number sold (in millions)
Jan.-Mar. 2012	152.7
Apr.-Jun. 2012	156.2
Jul.-Sep. 2012	179.7
Oct.-Dec. 2012	227.8
Jan.-Mar. 2013	222.6
Apr.-Jun. 2013	253.3
Jul.-Sep. 2013	276.6
Oct.-Dec. 2013	292.7
Jan.-Mar. 2014	288.4
Apr.-Jun. 2014	302.1
Jul.-Sep. 2014	332.6
Oct.-Dec. 2014	377.8
Jan.-Mar. 2015	334.4
Apr.-Jun. 2015	337.2
Jul.-Sep. 2015	355.2
Oct.-Dec. 2015	399.5

Formula used: $Relativefrequency=\frac{Frequency}{}$

  $Relativefrequency=\frac{Frequency}{ Sum\text{ of all }Frequency}$

Calculation:

From the given table,

The sum of all frequency is $4684.3$

The table of relative frequency is given by

Quarter	Number sold (in millions)	Relative Frequency
Jan.-Mar. 2012	152.7	$\frac{152.7}{4684.3}=0.033$
Apr.-Jun. 2012	156.2	$\frac{156.2}{4684.3}=0.035$
Jul.-Sep. 2012	179.7	$\frac{179.7}{4684.3}=0.040$
Oct.-Dec. 2012	227.8	$\frac{227.8}{4684.3}=0.051$
Jan.-Mar. 2013	222.6	$\frac{222.6}{4684.3}=0.050$
Apr.-Jun. 2013	253.3	$\frac{253.3}{4684.3}=0.056$
Jul.-Sep. 2013	276.6	$\frac{276.6}{4684.3}=0.062$
Oct.-Dec. 2013	292.7	$\frac{292.7}{4684.3}=0.065$
Jan.-Mar. 2014	288.4	$\frac{288.4}{4684.3}=0.064$
Apr.-Jun. 2014	302.1	$\frac{302.1}{4684.3}=0.067$
Jul.-Sep. 2014	332.6	$\frac{332.6}{4684.3}=0.074$
Oct.-Dec. 2014	377.8	$\frac{377.8}{4684.3}=0.084$
Jan.-Mar. 2015	334.4	$\frac{334.4}{4684.3}=0.074$
Apr.-Jun. 2015	337.2	$\frac{337.2}{4684.3}=0.075$
Jul.-Sep. 2015	355.2	$\frac{355.2}{4684.3}=0.079$
Oct.-Dec. 2015	399.5	$\frac{399.5}{4684.3}=0.089$

To determine

To construct: A relative frequency histogram.

Explanation of Solution

Given information:The following frequency distribution presents the number of smartphones (in millions) shipped in each quarter of each year from 2012 through 2015.

Quarter	Number sold (in millions)
Jan.-Mar. 2012	152.7
Apr.-Jun. 2012	156.2
Jul.-Sep. 2012	179.7
Oct.-Dec. 2012	227.8
Jan.-Mar. 2013	222.6
Apr.-Jun. 2013	253.3
Jul.-Sep. 2013	276.6
Oct.-Dec. 2013	292.7
Jan.-Mar. 2014	288.4
Apr.-Jun. 2014	302.1
Jul.-Sep. 2014	332.6
Oct.-Dec. 2014	377.8
Jan.-Mar. 2015	334.4
Apr.-Jun. 2015	337.2
Jul.-Sep. 2015	355.2
Oct.-Dec. 2015	399.5

Definition used:

Histogram based on relative frequency is called relative frequency histogram.

Solution:

Quarter	Number sold (in millions)	Relative Frequency
Jan.-Mar. 2012	152.7	$0.033$
Apr.-Jun. 2012	156.2	$0.035$
Jul.-Sep. 2012	179.7	$0.040$
Oct.-Dec. 2012	227.8	$0.051$
Jan.-Mar. 2013	222.6	$0.050$
Apr.-Jun. 2013	253.3	$0.056$
Jul.-Sep. 2013	276.6	$0.062$
Oct.-Dec. 2013	292.7	$0.065$
Jan.-Mar. 2014	288.4	$0.064$
Apr.-Jun. 2014	302.1	$0.067$
Jul.-Sep. 2014	332.6	$0.074$
Oct.-Dec. 2014	377.8	$0.084$
Jan.-Mar. 2015	334.4	$0.074$
Apr.-Jun. 2015	337.2	$0.075$
Jul.-Sep. 2015	355.2	$0.079$
Oct.-Dec. 2015	399.5	$0.089$

From the above table, the relative frequency histogram is given by

  

To determine

True or False: In each year, the quarter with the largest sales was October to December.

Answer to Problem 19E

True.

Explanation of Solution

Given information: The following frequency distribution presents the number of smartphones (in millions) shipped in each quarter of each year from 2012 through 2015.

Quarter	Number sold (in millions)
Jan.-Mar. 2012	152.7
Apr.-Jun. 2012	156.2
Jul.-Sep. 2012	179.7
Oct.-Dec. 2012	227.8
Jan.-Mar. 2013	222.6
Apr.-Jun. 2013	253.3
Jul.-Sep. 2013	276.6
Oct.-Dec. 2013	292.7
Jan.-Mar. 2014	288.4
Apr.-Jun. 2014	302.1
Jul.-Sep. 2014	332.6
Oct.-Dec. 2014	377.8
Jan.-Mar. 2015	334.4
Apr.-Jun. 2015	337.2
Jul.-Sep. 2015	355.2
Oct.-Dec. 2015	399.5

Solution:

From the given table we can say that in each year, the quarter with largest sales was from October to December.

Hence, it is true that in each year, the quarter with the largest sales was October to December.