Calculating Arithmetic Mean from Student Grades
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Questions and Answers

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

23

According to the table, what is the total of 'Pm x f'?

172.5

According to the table, what is the sum of 'Punto medio (Pm)'?

46.8

Based on the 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 sum of all values divided by the number of values.

Median

The central value separating the greater and lesser halves of a data sample.

Mode

The value that appears most frequently in a data set.

Frequency Distribution Table

A table that displays the frequency of various outcomes in a sample.

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Midpoint

The central value of a particular class interval.

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Calculating $\sum (P_m \times f)$

Multiply each midpoint by its frequency, then add these products.

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Calculating Arithmetic Mean from Grouped Data

Divide the sum of ($P_m \times f$) by the total number of students ($\sum f$).

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Interpreting Calculated Mean

The approximate average grade of the student group based on the provided data.

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Arithmetic Mean of Grades

$\frac{172.5}{23} \approx 7.5$

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Purpose of Calculating Mean

It provides one way to summarise the complex data into a single representative number.

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Study Notes

  • Student grades are presented in a table.

Table Details

  • Grades are in the first column
  • The quantity of students is in the second column
  • The midpoint is in the third column (Pm)
  • The product of the midpoint and quantity of students (Pm x f) is in the fourth column

Data in the Table

  • Grades 6.0 - 6.6, 7 students, midpoint of 6.3, Pm x f is 44.1
  • Grades 6.6 - 7.2, 4 students, midpoint of 6.9, Pm x f is 27.6
  • Grades 7.2 - 7.8, 5 students, midpoint of 7.5, Pm x f is 37.5
  • Grades 7.8 - 8.4, 1 student, midpoint of 8.1, Pm x f is 8.1
  • Grades 8.4 - 9.0, 1 student, midpoint of 8.7, Pm x f is 8.7
  • Grades 9.0 - 9.6, 5 students, midpoint of 9.3, Pm x f is 46.5
  • There are a total of 23 students
  • The sum of the midpoints is 46.8
  • The sum of all Pm x f values is 172.5

Question

  • Based on the above, what is the arithmetic mean of the grades of the group of students?

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Description

Calculate the arithmetic mean of student grades from a grouped frequency distribution. The grades, frequency, midpoint, and their products are given. Use these values to find the mean.

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