Math Problem Statement

vGroup

​10-under 20

​20-under 30

​30-under 40

​40-under 50

Frequency

55

77

99

44 approxiamte mean

Solution

To calculate the approximate mean for grouped data, we use the formula:

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

Where:

  • ff is the frequency for each group.
  • xx is the midpoint of each group (also called the class mark).

Step 1: Find the midpoints of each group.

  • For the group "10-under 20": midpoint x1=10+202=15x_1 = \frac{10 + 20}{2} = 15
  • For the group "20-under 30": midpoint x2=20+302=25x_2 = \frac{20 + 30}{2} = 25
  • For the group "30-under 40": midpoint x3=30+402=35x_3 = \frac{30 + 40}{2} = 35
  • For the group "40-under 50": midpoint x4=40+502=45x_4 = \frac{40 + 50}{2} = 45

Step 2: Multiply each midpoint by its corresponding frequency.

  • f1x1=5515=825f_1 \cdot x_1 = 55 \cdot 15 = 825
  • f2x2=7725=1925f_2 \cdot x_2 = 77 \cdot 25 = 1925
  • f3x3=9935=3465f_3 \cdot x_3 = 99 \cdot 35 = 3465
  • f4x4=4445=1980f_4 \cdot x_4 = 44 \cdot 45 = 1980

Step 3: Sum up the products and frequencies.

  • Sum of products: 825+1925+3465+1980=8195825 + 1925 + 3465 + 1980 = 8195
  • Sum of frequencies: 55+77+99+44=27555 + 77 + 99 + 44 = 275

Step 4: Calculate the approximate mean.

Mean=819527529.8\text{Mean} = \frac{8195}{275} \approx 29.8

So, the approximate mean is 29.8.

Would you like more details or explanations on any part of this?

Here are 5 questions for deeper understanding:

  1. How is the midpoint calculated for each group?
  2. What if the frequency distribution had more groups, how would it affect the mean?
  3. How does this method compare to calculating the mean for ungrouped data?
  4. What happens if the class intervals were unequal?
  5. Can this method be used for non-numerical data?

Tip: Always ensure the intervals are consistent and the frequencies cover all data points for accurate calculations!

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Math Problem Analysis

Mathematical Concepts

Statistics
Grouped Data
Mean Calculation

Formulas

Mean = (∑(f * x)) / ∑f

Theorems

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Suitable Grade Level

Grades 8-10