DIS - Measures of Central Tendency Lesson

Measures of Central Tendency

The science of collecting, organizing, and interpreting data in order to make decisions is called statistics. The first statistics we will look at you've probably seen before. The Measures of Central Tendency are mean, median, and mode. These measures deal with the center of a set of data.

Data - information about a product or process, usually in numerical form.
Statistics - the science of collecting, organizing, and interpreting data in order to make decisions.
Center - measures of center refer to the summary measures used to describe the most "typical" value in a set of data. The two most common measures of center are median and the mean.
Mean - or average is the sum of all of the data divided by the number of data values. The mean is often represented as $X$ .
Median - is the middle number, or average of the two middle numbers after the data values have been arranged in ascending or descending order.
Mode - is the data value that appears most often. There can be one mode, no mode, or more than one mode.

Given the following data set of values: 10, 2, 38, 23, 38, 23, 21, 48, 92

$LaTeX: Mean\:\:\overline x=\frac{10+2+28+23+28+23+21+48+92}{9} \\ \overline x \approx 32.78 \\ Median: 2, 10, 21, 23, \color{blue}23, \color{black}38, 38, 48, 92 \\ Mode: 23, 28$ $Mean\:\:\overline x=\frac{10+2+28+23+28+23+21+48+92}{9} \\ \overline x \approx 32.78 \\ Median: 2, 10, 21, 23, \color{blue}23, \color{black}38, 38, 48, 92 \\ Mode: 23, 28$

Introduction to Description and Inferential Statistics

In the following video, the concepts of descriptive and inferential statistics was discussed, as well as the following terms: average, arithmetic mean, median, and mode.

Mean, Median, and Mode

In the following video, an example is shown that computes the mean, median, and mode of a set of data.

Measures of Central Tendency Exploration (Videos 1 and 2 below)

In Video 1, an example is explored that is a practical application of the computation of the mean, median, and mode of a set of data. The first 3:03 of the video computes the mean. From 03:04 to 10:58 shows the computation of the median. From 10:59 to the end shows the mode. These examples make use of the TI-84 Plus Silver Edition.

In Video 2, four examples (labeled numbers 1, 2, 3, and 4) are shown computing the mean, median, and mode. They make use of the TI-30XS calculator.

Exploring Changes in Measures of Center (Video 3)

In Video 3, the first 05:13 shows two examples (numbered 5 and 6) computing the mean, median, and mode of sets of data, as well as discussing outliers and which measure of center is the best measure. From 05:14 to the end of the video, two more examples (numbered 7 and 8) are shown which explore how to compute a missing data point given the mean.

Comparing Means from Dot Plots

In this video, the means of two data sets are computed from two dot plots. The question, "the mean is a good measure for the center of the distribution of which data set?" is then explored.

Comparing the Mean and Median: Application Problem

In this video, an application problem with three parts is explored which then compares the median and the mean.

Impacts of Outliers on the Mean and Median (Video 1 and Video 2)

In Video 1, an application problem which explores the impact on the mean and median when an outlier on the left (lower value) is removed.

In Video 2, an application problem which explores the impact on the mean and median when an outlier on the right (higher value) is removed.

Measures of Central Tendency Practice

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