Math Problem Statement

A frequency table of grades has five classes​ (A, B,​ C, D,​ F) with frequencies of 22​, 1414​, 1515​, 77​, and 22 respectively. Using​ percentages, what are the relative frequencies of the five​ classes? Question content area bottom Part 1 Complete the table. Grade Frequency Relative frequency A 22 enter your response here​% B 1414 enter your response here​% C 1515 enter your response here​% D 77 enter your response here​% F 22 enter your response here​% ​(Round to two decimal places as​ needed.)

Solution

To find the relative frequency in percentages for each grade class, we need to follow these steps:

  1. Calculate the total frequency.
  2. Divide the frequency of each class by the total frequency.
  3. Convert the resulting ratio to a percentage by multiplying by 100.
  4. Round to two decimal places.

Step 1: Calculate the Total Frequency

Total Frequency=22+1414+1515+77+22=3030\text{Total Frequency} = 22 + 1414 + 1515 + 77 + 22 = 3030

Step 2: Calculate Relative Frequencies

For each grade:

  • A: Relative Frequency (A)=(223030)×100=0.7260.73%\text{Relative Frequency (A)} = \left(\frac{22}{3030}\right) \times 100 = 0.726 \approx 0.73\%
  • B: Relative Frequency (B)=(14143030)×100=46.67%\text{Relative Frequency (B)} = \left(\frac{1414}{3030}\right) \times 100 = 46.67\%
  • C: Relative Frequency (C)=(15153030)×100=49.92%\text{Relative Frequency (C)} = \left(\frac{1515}{3030}\right) \times 100 = 49.92\%
  • D: Relative Frequency (D)=(773030)×100=2.54%\text{Relative Frequency (D)} = \left(\frac{77}{3030}\right) \times 100 = 2.54\%
  • F: Relative Frequency (F)=(223030)×100=0.7260.73%\text{Relative Frequency (F)} = \left(\frac{22}{3030}\right) \times 100 = 0.726 \approx 0.73\%

Completed Table

GradeFrequencyRelative Frequency (%)
A220.73
B141446.67
C151549.92
D772.54
F220.73

Would you like more details or have any questions?

Here are five questions you might ask:

  1. How do you calculate the total frequency in a frequency table?
  2. What is the formula for calculating relative frequency?
  3. Why do we convert the relative frequency to a percentage?
  4. How do you round numbers to two decimal places?
  5. Can you explain how relative frequencies help in data analysis?

Tip: Always double-check your total frequency before calculating relative frequencies to avoid errors in your results.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Statistics
Frequency Tables
Percentage Calculations

Formulas

Relative Frequency Formula: \( \text{Relative Frequency} = \left(\frac{\text{Frequency}}{\text{Total Frequency}}\right) \times 100 \)

Theorems

-

Suitable Grade Level

High School