Statistics: Mean, Median, Mode Calculations

Illustration 1: Calculating Mean, Median, and Mode

• Data Set: 11, 12, 12, 14, 15, 15, 16, 17, 18, 18, 19, 20, 21, 22, 23
• Mean: The average of the data set; calculated by summing all values and dividing by the number of values.
• Median: The middle value when the data set is ordered; in this case, 16.
• Mode: The value(s) that appear most frequently; in this case, 12 and 15 (bimodal).

Illustration 2: Calculating the Mean of Grouped Data

• Data: Marks are grouped into intervals with their corresponding frequencies.
• Method: To find the mean, you need to compute the midpoint of each interval. Multiply each midpoint by its frequency, sum these products, and then divide by the total frequency.
• Midpoints: These are the central values of each interval (e.g., for the 0-10 interval, the midpoint is 5).

Median and Mode of Grouped Data

• Median: Identify the median class (class containing the middle data value) using cumulative frequency. Apply a formula to calculate the precise median value within the median class. This involves using the cumulative frequency and class width.
• Mode: Determine the modal class (the class with the highest frequency). The precise mode can be approximated using a formula. This involves considering the frequencies of neighboring classes.

Steps to Find the Median of Grouped Data:

• Cumulative Frequency: Add the frequencies consecutively to obtain the cumulative frequency for each class.
• Median Class: Determine the class where the cumulative frequency surpasses half the total frequency.
• Median Formula: Use the specific formula for calculating the median from grouped data; this formula utilizes the cumulative frequency, class width, and frequency of the median class.

This quiz covers the calculation of mean, median, and mode for both ungrouped and grouped data sets. Test your understanding of how to find averages and central tendencies using various methods, including the midpoint approach for grouped data. Improve your statistics skills by working through practical examples and illustrations.