Calculating Grade Averages
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Questions and Answers

According to the table, what is the total number of students?

  • 46.8
  • 23 (correct)
  • 172.5
  • 7

Based on the information provided, what is the sum of 'Pm x f' for all student groups?

172.5

Given the data in the table, what is the formula to calculate the arithmetic mean of the student grades?

  • Total number of students / Sum of Pm
  • Sum of Pm / Total number of students
  • Total number of students / Sum of (Pm x f)
  • Sum of (Pm x f) / Total number of students (correct)

Based on the data table, what is the arithmetic mean of the grades of the group of students?

<p>7.5</p> Signup and view all the answers

Flashcards

Arithmetic Mean

The average calculated by summing all values and dividing by the number of values.

Median

The central value in a dataset, separating the higher half from the lower half.

Mode

The value that appears most frequently in a dataset.

Frequency Distribution

A table that shows how many data points fall into specific intervals or categories.

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Class Midpoint

The midpoint of a class interval in a frequency distribution.

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Frequency (f)

The number of data points within a specific class interval.

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Pm × f

Multiplying the class midpoint by its corresponding the number of students value.

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Calculating the Mean (Grouped Data)

Sum of (Midpoint * Frequency) divided by the Total Number of Students

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What does the Arithmetic Mean represent?

Estimated average score of the group.

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Why use grouped data?

Using frequency distribution to find the mean provides an estimate when individual data points are unavailable.

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Study Notes

  • The grades of a group of students are presented in a table.
  • The table includes columns for grades ("Calificaciones"), number of students ("Cantidad de estudiantes" or f), midpoint ("Punto medio" or Pm), and Pm x f.
  • The grades are grouped into ranges: 6.0-6.6, 6.6-7.2, 7.2-7.8, 7.8-8.4, 8.4-9.0, and 9.0-9.6.
  • For the 6.0-6.6 range, there are 7 students and a midpoint of 6.3 which equals 44.1 when multiplied.
  • For the 6.6-7.2 range, there are 4 students and a midpoint of 6.9 which equals 27.6 when multiplied.
  • For the 7.2-7.8 range, there are 5 students and a midpoint of 7.5 which equals 37.5 when multiplied.
  • For the 7.8-8.4 range, there is 1 student and a midpoint of 8.1 which equals 8.1 when multiplied.
  • For the 8.4-9.0 range, there is 1 student and a midpoint of 8.7 which equals 8.7 when multiplied.
  • For the 9.0-9.6 range, there are 5 students and a midpoint of 9.3 which equals 46.5 when multiplied.
  • The total number of students is 23.
  • The sum of the midpoints is 46.8
  • The sum of the Pm x f values is 172.5
  • The question asks for the arithmetic mean of the grades of the student group.

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Description

This lesson shows how to calculate grade averages from a table. The data includes student grades, number of students per grade range, and midpoint values. We sum the products of midpoints and frequencies, then divide by the total number of students.

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