MIA U2D7 Warmup: Find the mean (rounded to the nearest tenth) and median for the following data: 73, 50, 72, 70, 70, 84, 85, 89, 89, 70, 73, 70, 72, 74 Mean: 74.4 Median: 72.5 Collect Interims!!!

Homework Check: Document Camera How to calculate one variable statistics on the – Ti-83+ Ti-83+ – Ti-84+ or on next slide Ti-84+

Common Core Math I Unit 2: One-Variable Statistics Boxplots, Interquartile Range, and Outliers; Choosing Appropriate Measures

Objective Students will be able to… Interpret data based on the shape of a data distribution Choose the appropriate measures of center (mean or median) and spread (standard deviation or interquartile range) to describe the distribution. Interpret summary statistics for center and spread in the context of the data.

Quantitative Data Dotplot Histogram Boxplot Describing Data Graphically S-ID.1 Represent data with plots on the real number line (dot plots, histograms, and box plots).

Describing Data Numerically – Unit 1 Measures of Center – mean, median Measures of Spread – range, interquartile range, standard deviation S-ID.2 Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.

Boxplots! Measures of Spread - YouTube

Boxplots Min Q 1 Median Q 3 Max Lower Upper Quartile Quartile

Practice! Below is a stem and leaf plot of the amount of money spent by 25 shoppers at a grocery store. StemLeaf Key: 4  2 = $42

Practice! a)Calculate the mean and median. b)Calculate the lower and upper quartiles and IQR. c)Determine which, if any, values are outliers. d)Write several sentences to describe this data set in context. e)Name some factors that might account for the extreme values, and the much lower measure of center. StemLeaf Key: 4  2 = $42

U2D7 Group Activity Boxplots and Outliers Teacher completes with class

Describing Data Two ways to describe data: Graphically Dot plot Histogram – Boxplot Numerically – Measures of Center: Median and Mean – Measures of Spread

Measures of Spread Range Interquartile Range (IQR) Standard Deviation How much do values typically vary from the center?

Thinking about the Situation Consider the following test scores: Who is the best student? How do you know? StudentTest 1Test 2Test 3Test 4 Johnny Will Anna

Measures of Spread One-Variable: Range Interquartile Range (IQR) Mean Absolute Deviation (MAD) Standard Deviation How much do values typically vary from the center?

ScoreMean Deviation from the Mean Anna Test 1 Test 2 Test 3 Test 4 Investigation 1: Deviation from the Mean

So what exactly is deviation? (-4) + (-3) + (-1) = -8(+5 ) + (+3) = +8

Measure of Spread Sum of deviations = (-4)+(-3)+(-1)+(+5)+(+3) Average of the deviations= = 0 An average deviation of zero means that there is no variability! Houston, we have a problem!

How can we fix our problem? Take the absolute value of each distance/deviation and then find the average So the average distance or deviation from the mean is about 3 points (above or below). This is called the Mean Absolute Deviation, or MAD

Mean Absolute Deviation

How can we fix our problem? Investigation 2: Mean Absolute Deviation Deviation from the Mean Absolute Deviation from the Mean Johnny Test 1 Test 2 Test 3 Test 4 Will Test 1 Test 2 Test 3 Test 4 Anna Test 1 Test 2 Test 3 Test 4

Square each deviation and then find the average of the squared deviations. This is called the standard deviation.

Back to Johnny, Will and Anna... Investigation 3: Calculating the Standard Deviation StudentTest 1Test 2Test 3Test 4 Johnny Will Anna

Who is the best student? How do you know? StudentTest 1Test 2Test 3Test 4 Test Average Standard Deviation Johnny Will Anna

Assignments: Homework 1: U2D7 Boxplots and Outliers Practice Homework 2: U2D7 HMWK WS