Math Problem Statement

Calculate the Mean, Median, Mode, and Average Deviation for the given class limits and frequency distribution.

Solution

Let's go through each of the steps required to solve the following:

Given Data:

Class Limits and Frequencies:

  • 34 - 96 → 13
  • 97 - 159 → 2
  • 160 - 222 → 0
  • 223 - 285 → 5
  • 286 - 348 → 1
  • 349 - 411 → 1
  • 412 - 474 → 0
  • 538 - 600 → 1

We need to calculate:

  1. Mean
  2. Median
  3. Mode
  4. Average Deviation

I'll first calculate the midpoints for each class, as they will be needed to compute the mean and average deviation. Then, I'll solve each question one by one.

Let me work through these calculations.Here are the calculations based on the data provided:

  1. Mean: 158.13
  2. Median: 88.85
  3. Mode: 65.0
  4. Average Deviation: 110.52

Would you like more details on any of these steps or have additional questions?

Here are 5 related questions:

  1. How is the median class determined in grouped data?
  2. Why is the midpoint used when calculating the mean for grouped data?
  3. What is the difference between mean and median in a frequency distribution?
  4. How do we interpret the mode in this dataset?
  5. How does average deviation differ from standard deviation?

Tip: The average deviation gives a simple measure of spread but is less commonly used than standard deviation, which takes into account the square of differences from the mean.

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Math Problem Analysis

Mathematical Concepts

Statistics
Grouped Data Analysis
Frequency Distribution
Central Tendency
Dispersion

Formulas

Mean = Σ(f * x) / Σf
Median Class: L + [(N/2 - CF) / f] * h
Mode = L + [(f1 - f0) / (2f1 - f0 - f2)] * h
Average Deviation = Σ|x - Mean| / N

Theorems

Central Tendency Theorem
Median and Mode formulas for grouped data

Suitable Grade Level

Grades 10-12