EXAMPLE 9 Frequency distribution and relative frequency distribution for discrete data

The Recording Industry Association of America (RIAA) awards multi-platinum status for any musical recording that sells more than 2 million copies. Table 17 contains a random sample of 20 of the musical artists with the most multi-platinum singles.

Table 2.44: TABLE 17 Number of multi-platinum singles
Artist Multi-platinums Artist Multi-platinums
Beyoncé 4 Linkin Park 2
Bruno Mars 4 Madonna 2
Chris Brown 2 Michael Jackson 1
Elton John 1 Nicki Minaj 2
Fergie 3 Red Hot Chili Peppers 2
Jay-Z 4 Shakira 1
Justin Timberlake 1 Sugarland 1
Kanye West 7 Taylor Swift 8
Katy Perry 8 The Beatles 4
Lady Gaga 6 Tim McGraw 2
Table 2.44: Source: RIAA.

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Use this raw data to construct a frequency distribution and a relative frequency distribution of the number of multi-platinum singles.

Solution

We begin by making a tally of how many artists had one multi-platinum, how many had two, and so on. We then construct the frequency distribution for the variable Multiplatinums. Finally, we construct the relative frequency distribution by dividing the frequency by the total number of observations, 20. See Table 18.

Table 2.45: TABLE 18 Frequency distribution and relative frequency distribution of Multi-platinums
Multi-platinums Tally Frequency Relative frequency
1 image 5
2 image 6
3 | 1
4 |||| 4
5 0
6 | 1
7 | 1
8 || 2
Total 20

NOW YOU CAN DO

Exercises 9–12.