Lesson 8.1.1 – Teacher Notes Standard: 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, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable. Full mastery can be expected by the end of the chapter. Lesson Focus: The focus of this lesson is to refresh 6th grade skill of histograms, box plots, measures of center, variability, and shape. Problems 8-1 to 8-4 could be skipped or consolidated to shorten the lesson to one day. The emphasis needs to be placed on comparing data sets. (8-5, particularly part c) I can compare two numerical data distributions on a graph by visually comparing data displays, and assessing the degree of visual overlap. Calculator: Yes Literacy/Teaching Strategy: Turn and Talk (Whole lesson); Huddle (Struggling Learners) .

Data Analysis Unit Representing Data Lesson 8.1.1 Data Analysis Unit Representing Data Goal: I can represent data with plots on the real number line (dot plots, histograms, and box plots). S-ID.1

Objective - To make and interpret box-and-whisker plots used to represent data. 19 13 3 10 15 20 18 10 12 13 16 17 . Write the data in increasing order from smallest to largest. 3 10 10 12 13 13 15 16 17 18 19 20 Median lower half of data upper half of data 13 +15 = 14 2 Median of lower half Median of upper half 10 +12 17 +18 Lower Quartile Upper Quartile = = 11 = = 17.5 2 2

Drawn from the minimum to the maximum. (Whiskers) 3 10 12 13 15 16 17 18 19 20 Median = 14 Lower Quartile = 11 Upper = 17.5 . 0 5 10 15 20 25 Lower Quartile 11 Median 14 Upper Quartile 17.5 Maximum 20 Minimum 3 Range - Drawn from the minimum to the maximum. (Whiskers) Interquartile Range - Drawn from lower quartile to upper quartile. (Box)

Make a box-and-whisker plot to represent the data below. 11 2 5 7 6 13 25 8 11 12 22 Write the data in increasing order from smallest to largest. 2 5 6 7 8 11 11 12 13 22 25 Lower Quartile 6 Median 11 Upper Quartile 13 0 5 10 15 20 25

The box-and-whisker plots below represent the quiz scores from two different pre-algebra classes. What can you tell about how different the classes are? Period 2 0 5 10 15 20 25 Period 4 0 5 10 15 20 25 Period 4 performed better as a group with higher median, upper quartile, and lower quartile. The period 4 scores are also more tightly grouped together. Period 2 scores are more spread out.

Use the box-and-whisker plot below to find the following. 0 10 20 30 40 50 60 a) Minimum = 12 e) Upper Quartile = 46 b) Maximum = 61 f) Lower Quartile = 24 61 - 12 c) Range = = 49 g) Interquartile Range = 46 - 24 = 22 d) Median = 39

Make a box-and-whisker plot to represent the data below. 25 40 22 16 50 35 24 37 44 48 Write the data in increasing order from smallest to largest. 16 22 24 25 35 37 40 44 48 50 Median Lower Quartile 24 35 +37 Upper Quartile 44 = 36 2 0 10 20 30 40 50 60

Steps Order the data from least to greatest. Find the minimum and maximum values. Find the median. Find the lower and upper quartiles (medians of the lower and upper half). Plot these five numbers below a number line. Draw the box, whiskers, and a line segment through the median.

If there is an even data set…

Box and Whisker Plot Box plot A box plot is a concise graph showing the five point summary. Multiple box plots can be drawn side by side to compare more than one data set. Advantages Shows 5-point summary and outliers Easily compares two or more data sets Handles extremely large data sets easily. Disadvantages Not as visually appealing as other graphs Exact values other than min, max and median can not be determined from box plot.

Box Plot A box encloses the middle half of the data and whiskers extend to the minimum and maximum data values median Q1 Q3 max min

Five point spread……

Box Plot

Box Plot

We can describe data by talking about: Mean – (Average) adding all the numbers up and dividing by the total number of numbers. Median – the number found in the middle after arranging them from least to greatest Mode – the number repeated the most Range – the difference found by subtracting the least number from the greatest number.

Whether we are talking about a Dot plot, Histogram, Bar graph we can describe the shape.

Is this symmetrical?

In some cases you can have an outlier… In some cases you can have an outlier….. A number situated away or detached from the main body or system of numbers

Dot Plot Dot plot A dot plot can be used as an initial record of distinct categorical data values. The range determines a number line which is then plotted with X’s (or dots) for each data value. Advantages Quick analysis of data Shows range, minimum & maximum, gaps & clusters, and outliers easily Can determine exact values. Disadvantages Not as visually appealing Best for under 50 data values Needs small range of data

Dot Plots How many of each color of M&M are in a package Frequency Colors

Dot Plot for the Number of M&M's™ in a Package   12 13 14 15 16 17 18 19 20 21 22 23 Frequency Number of M&M in a Package Graph paper is a good idea for it is crucial that each recorded X be uniform in size and placed exactly across from each other (one-to-one correspondence). Notice the cluster at 17 & 18 as well as the gap at 13 and 22. The mode is 18, the median is the second X from the bottom for number 18, and the mean is 17.68 or 18.

Dot Plot made from a Tally Chart

What do you notice about the difference of a Histogram and a Bar Graph???

Bar Graph Bar Graph A Bar Graph is a type of graph that displays data with individual columns. Categories that measure such things as time, inches, temperature, etc. Bars have the same width and have space between each bar. Advantages Visually strong Can compare to normal curve Usually vertical axis some will have a horizonal axis and you are able to distinctively see the frequency count of each item. Disadvantages Often require additional explanation .

Histograms Histogram A histogram is a type of bar graph that displays continuous data in ordered columns called intervals. Categories are of continuous measure such as time, inches, temperature, etc. Bars have the same width and are drawn next to each other with no gaps. Advantages Visually strong Can compare to normal curve Usually vertical axis is a frequency count of items falling into each category. Disadvantages Cannot read exact values from histogram because data is grouped into categories. More difficult to compare two data sets. Use only with continuous data (intervals). .

Histograms In a histogram, data are grouped into intervals of EQUAL width. The number of data values in each interval is the frequency of the interval. To draw, begin by using a frequency chart (tally chart) and making a frequency distribution (intervals). Histogram typically contain 5-10 intervals. .

Histograms 2009-2010 Mean SAT Math Scores

Histogram  

Relating Histograms to Box Plots . http://higheredbcs.wiley.com/legacy/college/mann/0470444665/ap plets/applet_01_v4.html

Day II How to analyze data of a box plot. https://learnzillion.com/lesson_plans/6527-compare-box-plots-using- center-and-spread/lesson How to interpret Histograms https://learnzillion.com/lesson_plans/6826-interpreting-histograms/ Observing symmetry, bell curves and skews. https://learnzillion.com/lesson_plans/7751/ .

Dot Plot http://stattrek.com/statistics/charts/dot-plot.aspx?tutorial=ap

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