Smartphone sales: The following frequency distribution presents the number of smartphones (in millions) shipped in each quarter of each year from 2012 through 2015.
- Construct a frequency bar graph.
- Construct a relative frequency distribution.
- Construct a relative frequency bar graph.
- True or false: In each year, the quarter with the largest sales was October to December.
a.
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
b.
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:
Calculation:
From the given table,
The sum of all frequency is
The table of relative frequency is given by
Quarter | Number sold (in millions) | Relative Frequency |
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 |
c.
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 | |
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 |
From the above table, the relative frequency histogram is given by
d.
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.
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