Central Tendency  Key Learnings: Statistics is a branch of mathematics that involves collecting, organizing, interpreting, and making predictions from data  UEQ: How do we summarize and organize data?

Measures of Central Tendency  LEQ: How do we find the measures of central tendency for a set of data?  Vocab: Mean Median Mode Range

Some Definitions  Mean – (average), the sum of all the values divided by the number of values  Median – (middle), the middle number when the values are arranged in order If there are 2 numbers in the middle, take their mean

Some More Definitions  Mode – (most), the most occurring of the group of data. There can be zero, one, or more than one mode.  Range – the largest number minus the smallest number

Try This…  Ex 1) Find the mean, median, mode, and range of the following amounts… $525, $500, $650, $600, $500, $675, $650, $500  Mean = $  Median = $  Mode = $  Range = $

Graphing Data  LEQ: How do we recognize which graph is most useful for a set of data?  Vocab: Frequency Table Stem-and-Leaf Plot Histogram Relative Frequency Circle Graph

Frequency Table  A frequency table organizes values to show the number of times each one appears  They look like this…

Stem-and-Leaf Plots  …are a quick way to arrange a set of data and view its shape or distribution  A key in the top corner shows how the numbers are split up  They can look like this…

Try it, you’ll like it…  Make a Stem-and-Leaf Plot for the data: 45, 67, 78, 54, 87, 56, 84, 90, 95, 53, 87, 63  A couple more things about them…  They show the median and mode easily  If you have larger numbers, the units digit is the leaf Example… 135 => 13 | 5

Histograms (Bar Graphs)  They show the frequency of data

If you think about it…a Histogram is just a Stem-and- Leaf Plot chart turned sideways

Work  Page 778 #

Box and Whisker Plot  LEQ: How do we create and interpret Box and Whisker Plots?  Vocab: Quartiles Range Interquartile Range Outlier 5-Number Summary

What are they for…  A Box and Whisker plot basically spreads out the data into 4 sections.  Each quarter holds 25% of the data.

How is it split up  There are 5 points that break the data… Minimum Value 1 st Quartile – Q1 Median – Q2 3 rd Quartile – Q3 Maximum Value

So what do I do?  Put the data in order.  Find the median.  Without using the median, find the upper (Q3) and lower (Q1) medians.  Draw and label a number line that includes all of your data.  Plot your points above the line and connect the dots.

More notes…  The Range = Maximum – Minimum  The Interquartile Range (IQR) = Q3 – Q1  If 2 numbers are in the middle, meet halfway like you did before

Try This…       Draw a Box and Whisker Plot and find the range and IQR.  Min = 25Q1 = 28Med = 30.5  Q3 = 34Max = 38  Range = 13IQR = 6

Work = p205 # 8, 9, 10, 12, 14

1.5 – Scatter Plots and Least-Square Lines  LEQ: How do we draw conclusions about correlation between variables?  Vocab: Scatter Plot Correlation Correlation Coefficient Least-Square Lines

Scatter Plots…  show a relationship between 2 variables.  Some real-world examples could be Age vs Height or Time vs Distance

Least-Square Line…  also called a Line of Best Fit.  Imagine a line going right through all of the points, like an average.

Correlation…  is a description about how the data points cluster together.

Correlation Coefficient…  …is denoted by ‘r’ and indicates how closely the data points cluster.  It is a value that can vary from -1 to 1.  A perfect negative correlation is r = -1.  A perfect positive correlation is r = 1.  The tighter the cluster of points, the closer the correlation is to +1 or -1.

For example…

Work  Page 41  #13, 14- Graph the points and draw a Line of Best Fit. Is the correlation weak or strong, positive or negative.  #15-20 – Match the r values with the correct graph.