A partir de lo anterior, ¿cuál es la media aritmética de las calificaciones del grupo de estudiantes?
Understand the Problem
La pregunta nos pide calcular la media aritmética de las calificaciones de un grupo de estudiantes, utilizando los datos proporcionados en la tabla. La tabla muestra los intervalos de calificaciones, la frecuencia de cada intervalo (cantidad de estudiantes), el punto medio de cada intervalo (Pm) y el producto del punto medio por la frecuencia (Pm x f). Para calcular la media aritmética, utilizaremos la fórmula: Media = Suma(Pm x f) / Suma(f).
Answer
La media aritmética es $7.5$.
Answer for screen readers
La media aritmética de las calificaciones del grupo de estudiantes es $7.5$.
Steps to Solve
- Identify the necessary values from the table
The problem provides a table containing the sum of the frequencies (cantidad de estudiantes), $\sum f = 23$, and the sum of the product of the midpoint and frequency, $\sum (Pm \times f) = 172.5$.
- Apply the formula for the arithmetic mean
The arithmetic mean (media aritmética) is calculated by dividing the sum of the product of the midpoint and frequency by the sum of the frequencies:
$$ \text{Mean} = \frac{\sum (Pm \times f)}{\sum f} $$
- Plug in the values and calculate the mean
Substitute the values from the table into the formula:
$$ \text{Mean} = \frac{172.5}{23} $$
- Calculate the result
$$ \text{Mean} = 7.5 $$
La media aritmética de las calificaciones del grupo de estudiantes es $7.5$.
More Information
The arithmetic mean represents the average score of the group, considering both the values within each interval and the number of students in each interval.
Tips
A common mistake is to sum all the midpoints (Pm) and divide by the number of midpoints, which does not account for the frequency of each interval. Another mistake is to confuse which values to use from the table.
AI-generated content may contain errors. Please verify critical information
