STAT 2 Central Tendency Measures: Mean, Median, and Mode in Data Analysis

What is the purpose of measures of central tendency?

To determine the average score of a group of scores.

What is the mean?

The most commonly used measure of the center of data, also known as the arithmetic average.

How is the population mean calculated?

Using the formula μ = ΣX / N, where μ is the population mean, ΣX is the sum of all scores, and N is the number of scores.

How is the sample mean calculated?

Using the formula x̄ = ΣX / n, where x̄ is the sample mean, ΣX is the sum of all scores, and n is the number of scores.

What is the formula for calculating the mean for ungrouped data?

x̄ = ΣX / n, where x̄ is the mean, ΣX is the sum of scores, and n is the number of scores.

What is grouped data?

Data or scores that are arranged in a frequency distribution.

What is frequency in the context of grouped data?

The number of observations falling in a category.

What is the midpoint method for calculating the mean of grouped data?

The formula X̄ = Σ(fX̄m) / n, where f is the frequency and X̄m is the midpoint of each class.

What are the steps to solve the mean for grouped data?

1. Find the midpoint of each class. 2. Multiply frequency by the class mark. 3. Sum the results. 4. Solve for the mean.

What is the median?

The value that divides the scores in the distribution into two equal parts.

How do you find the median of ungrouped data?

Arrange the scores in order and determine the middle score; if n is even, average the two middle scores.

What is the formula for calculating the median for grouped data?

X = LB + (n/2 - cf) / fm * c.i, where LB is the lower boundary of the median class, cf is cumulative frequency before the median class, fm is frequency of the median class, and c.i is the size of the class interval.

What is the mode?

The score or scores that occur most frequently in the distribution.

What are the classifications of mode?

Unimodal (one mode), Bimodal (two modes), Trimodal (three modes), and Multimodal (more than two modes).

What is the formula for calculating the mode for grouped data?

X = LB + (d1 / (d1 + d2)) * c.i, where LB is the lower boundary of the modal class, d1 is the difference between the frequency of the modal class and the frequency above it, d2 is the difference between the frequency of the modal class and the frequency below it, and c.i is the size of the class interval.

What is the significance of the cumulative frequency in median calculations?

It helps identify the median class by accumulating frequencies up to the median.

How do you calculate the mean from a frequency distribution table?

By using the midpoint method and applying the formula for grouped data.

What is the first step in finding the median for grouped data?

Complete the table for cumulative frequency.

What is the importance of the lower boundary in median calculations?

It is used to determine the starting point for calculating the median within the median class.

What is an example of calculating the mean for grouped data?

For scores of 40 students, using the frequency distribution to find the mean value.

What is the role of class intervals in calculating mode?

They help identify the modal class, which contains the highest frequency.

What does n/2 represent in median calculations?

It represents half of the total number of observations, used to find the median position.

What is the significance of the mode in data analysis?

It indicates the most common score, providing insight into the data distribution.