Math Problem Statement

The scores from 50 psychology students that took a standardized test are summarized in the given table.

Scores

Frequency

140 - 149

7

150 - 159

12

160 - 169

8

170 - 179

6

180 - 189

17

If a relative frequency distribution is constructed for this data set, what is the relative frequency for the fourth class, 170 - 179? Round the answer to two decimal places.

Relative frequency = 

Solution

To calculate the relative frequency for the fourth class (170 - 179), follow these steps:

  1. Determine the total number of students: Total number of students=7+12+8+6+17=50\text{Total number of students} = 7 + 12 + 8 + 6 + 17 = 50

  2. Identify the frequency of the fourth class:

    • The frequency for the class 170 - 179 is 6.
  3. Calculate the relative frequency: Relative frequency=Frequency of the classTotal number of students=650=0.12\text{Relative frequency} = \frac{\text{Frequency of the class}}{\text{Total number of students}} = \frac{6}{50} = 0.12

Thus, the relative frequency for the fourth class (170 - 179) is 0.12.

Would you like more details or have any questions? Here are some related questions:

  1. How do you interpret the relative frequency in the context of this problem?
  2. What is the sum of all relative frequencies for a distribution?
  3. How would you calculate the relative frequency for a class if the frequency and total number of data points are known?
  4. What is the importance of rounding when calculating relative frequencies?
  5. How could you visualize this data to better understand the distribution?

Tip: Always ensure that the sum of all relative frequencies in a distribution equals 1 (or 100% when expressed as a percentage).

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Math Problem Analysis

Mathematical Concepts

Statistics
Relative Frequency
Frequency Distribution

Formulas

Relative frequency = (Frequency of the class) / (Total number of students)

Theorems

Sum of all relative frequencies equals 1

Suitable Grade Level

Grades 9-12