In this math video we will learn about measures of center and measures of variability. We will define and learn about box plots or box and whisker plots, as well as dot plots or line plots. We will also learn about and define measure of center which are an average; a single value that is used to represent a collection of data using median and mean. Median is the middle number in a set of numbers that are listed in order. Mean is the arithmetic average of a distribution, obtained by adding the scores and then dividing by the number of scores. We will discover that Measures of Variability are how spread out the values are from each other and from the mean using range, IQR, and MAD. Range is the difference between the maximum and minimum. IQR is the range of the middle​ half of the data set. And, MAD is the average distance between each data value and the mean. We will define and practice finding each of these measures of center and variability. We will also review how to read double box plots and double line plots. We will compare data sets using measures of center and measures of variability. Student practice is embedded in the lesson with exemplar solutions.
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00:00 Introduction
00:16 Lesson Objectives
00:31 Essential Question
00:42 What is a Box Plot?
02:10 Lower and Upper Quartile of Data
03:20 What is a Line or Dot Plot?
04:33 What are Measures of Center?
04:48 What is Median?
04:54 What is Mean?
05:09 What are Measures of Variability
05:28 What is Range?
05:34 What is IQR?
05:40 What is MAD?
05:51 Find Median on a Box Plot
06:38 Find Median from a Dot Plot
07:38 Find Mean from a Dot Plot
08:41 Find Range from a Box Plot
09:25 Find the Range from a Dot Plot
09:46 Find IQR
10:55 Find MAD - Mean Absolute Deviation
13:10 Compare Data Sets Using Double Box Plots
14:40 Compare Data Sets Using Double Dot Plots
16:41 Student Practice - Compare MAD
18:50 The Solution
Statistics and Probability 7.SP
7.SP.B. Draw informal comparative inferences about two populations.
7.SP.B.3. Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team and both distributions have similar variability (mean absolute deviation) of about 5 cm. The difference between the mean heights of the two teams (10 cm) is about twice the variability (5 cm) on either team. On a dot plot, the separation between the two distributions of heights is noticeable.
7.SP.B.4. Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.