Math Problem Statement

Calcular la media usando la tabla de frecuencia con valores de x y f, donde x = [21, 22, 23, 24, 25] y f = [18, 6, 16, 20, 1].

Solution

To calculate the mean (or "media") from the given data, we use the formula for the mean of grouped dataTo calculate the mean (or "media") from the given data, we use the formula for the mean of grouped

Mean=(xf)f\text{Mean} = \frac{\sum (x \cdot f)}{\sum f}

Where:

  • xx is the value of the variable (the "x" column).
  • ff is the frequency (the "f" column).

Steps:

  1. Multiply each value of xx by its corresponding frequency ff.
  2. Add these products together.
  3. Divide the result by the sum of the frequencies.

Let's calculate:

(xf)=(2118)+(226)+(2316)+(2420)+(251)\sum (x \cdot f) = (21 \cdot 18) + (22 \cdot 6) + (23 \cdot 16) + (24 \cdot 20) + (25 \cdot 1) =378+132+368+480+25=1383= 378 + 132 + 368 + 480 + 25 = 1383

f=18+6+16+20+1=61\sum f = 18 + 6 + 16 + 20 + 1 = 61

Now, calculate the mean:

Mean=13836122.7\text{Mean} = \frac{1383}{61} \approx 22.7

So, the mean is approximately 22.7 (rounded to one decimal place).

Would you like further details or have any questions?

Related Questions:

  1. What is the median of this data set?
  2. How would the mean change if the frequency of x=25x = 25 were higher?
  3. Can you calculate the variance for this grouped data?
  4. How does the mean compare to the mode of the data set?
  5. What is the importance of using frequencies when calculating the mean?

Tip:

Always double-check the total frequency sum when calculating the mean to ensure accuracy.

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Math Problem Analysis

Mathematical Concepts

Statistics
Mean
Frequency Distribution

Formulas

Mean = Σ(x * f) / Σf

Theorems

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Suitable Grade Level

Grades 6-8