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QuestionFind the relative frequencies (in %) for grades A, B, C, D, F with frequencies 3,14,17,6,23, 14, 17, 6, 2. Round to two decimal places.

Studdy Solution

STEP 1

Assumptions1. The frequencies of the grades are given as A =3, B =14, C =17, D =6, F =. We need to find the relative frequencies of each grade as a percentage3. The relative frequency is calculated as the frequency of a class divided by the total frequency, multiplied by100

STEP 2

First, we need to find the total frequency. We can do this by adding up the frequencies of all the classes.
Total frequency=Frequency of A+Frequency of B+Frequency of C+Frequency of D+Frequency of FTotal\, frequency = Frequency\, of\, A + Frequency\, of\, B + Frequency\, of\, C + Frequency\, of\, D + Frequency\, of\, F

STEP 3

Now, plug in the given values for the frequencies of the grades to calculate the total frequency.
Total frequency=3+14+17+6+2Total\, frequency =3 +14 +17 +6 +2

STEP 4

Calculate the total frequency.
Total frequency=3+14+17+6+2=42Total\, frequency =3 +14 +17 +6 +2 =42

STEP 5

Now that we have the total frequency, we can calculate the relative frequency of each grade. The relative frequency is calculated as the frequency of a class divided by the total frequency, multiplied by100.
Relative frequency of A=Frequency of ATotal frequencytimes100%Relative\, frequency\, of\, A = \frac{Frequency\, of\, A}{Total\, frequency} \\times100\%

STEP 6

Plug in the values for the frequency of A and the total frequency to calculate the relative frequency of A.
Relative frequency of A=342times100%Relative\, frequency\, of\, A = \frac{3}{42} \\times100\%

STEP 7

Calculate the relative frequency of A.
Relative frequency of A=342times100%=7.14%Relative\, frequency\, of\, A = \frac{3}{42} \\times100\% =7.14\%

STEP 8

Repeat the same process for the remaining grades.
Relative frequency of B=Frequency of BTotal frequencytimes100%Relative\, frequency\, of\, B = \frac{Frequency\, of\, B}{Total\, frequency} \\times100\%Relative frequency of B=1442times100%=33.33%Relative\, frequency\, of\, B = \frac{14}{42} \\times100\% =33.33\%Relative frequency of C=Frequency of CTotal frequencytimes100%Relative\, frequency\, of\, C = \frac{Frequency\, of\, C}{Total\, frequency} \\times100\%Relative frequency of C=1742times100%=40.48%Relative\, frequency\, of\, C = \frac{17}{42} \\times100\% =40.48\%Relative frequency of D=Frequency of DTotal frequencytimes100%Relative\, frequency\, of\, D = \frac{Frequency\, of\, D}{Total\, frequency} \\times100\%Relative frequency of D=642times100%=14.29%Relative\, frequency\, of\, D = \frac{6}{42} \\times100\% =14.29\%Relative frequency of F=Frequency of FTotal frequencytimes100%Relative\, frequency\, of\, F = \frac{Frequency\, of\, F}{Total\, frequency} \\times100\%Relative frequency of F=242times100%=4.76%Relative\, frequency\, of\, F = \frac{2}{42} \\times100\% =4.76\%The relative frequencies of the grades are as followsA =7.14%, B =33.33%, C =40.48%, D =14.29%, F =4.76%

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