A frequency table grades have five classes (A,B,C,D,F) with frequencies of 5,11,14,7, and 3 respectively. Using percentages, what are the relative frequencies of the five classes

To find the relative frequency, the specific frequency is divided by the total frequency. To find in the percentages, the division is multiplied by 100

So,

Total frequencies = 5+11+14+7+3 = 40

So,

[tex]Relative-frequency\ of\ A = \frac{5}{40} *100\\= 0.125*100\\=12.5\%\\Relative-frequency\ of\ B = \frac{11}{40} * 100\\= 0.275*100\\=27.5\%\\Relative-frequency\ of\ C = \frac{14}{40} * 100\\=0.35*100\\=35\%\\Relative-frequency\ of\ D = \frac{7}{40} * 100\\=0.175*100\\=17.5\%\\Relative-frequency\ of\ E= \frac{3}{40} * 100\\=0.075*100\\=7.5\%[/tex]

Hence,

The relative frequencies using percentages are as follows:

A => 12.5%

B => 27.5%

C => 35%

D => 17.5%

E => 7.5%

Keywords: Frequency, relative frequency

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psm22415 psm22415 · Answer 2 · 2022-01-22T03:16:16+01:00

The relative frequencies of the five classes are 12.5%, 27.5%, 35%, 17.5%, 7.5%.

Given that

A frequency table grades have five classes (A, B, C, D, F) with frequencies of 5,11,14,7, and 3 respectively.

We have to determine

Using percentages, what are the relative frequencies of the five classes.

According to the question

The relative frequency, the specific frequency is divided by the total frequency.

The sum of all the frequencies is called relative frequency.

= 5 + 11 +14 +7 +3 = 40

Then,

The relative frequency of the first class is,

[tex]= \dfrac{5}{40} \times 100\\ \\ = 0.125 \times 100\\ \\ =12. 5 \rm \ Percent[/tex]

The relative frequency of the second class is,

[tex]= \dfrac{11}{40} \times 100\\ \\ = 0.275 \times 100\\ \\ =27. 5 \rm \ Percent[/tex]

The relative frequency of the third class is,

[tex]= \dfrac{14}{40} \times 100\\ \\ = 0.35 \times 100\\ \\ =35 \rm \ Percent[/tex]

The relative frequency of the fourth class is,

[tex]= \dfrac{7}{40} \times 100\\ \\ = 0.175 \times 100\\ \\ =17. 5 \rm \ Percent[/tex]

The relative frequency of the fifth class is,

[tex]= \dfrac{3}{40} \times 100\\ \\ = 0.075 \times 100\\ \\ =7. 5 \rm \ Percent[/tex]

Hence, the relative frequencies of the five classes are 12.5%, 27.5%, 35%, 17.5%, 7.5%.

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