Section 7.7Statistics and Statistical Graphs

Data Collection

Pulse Rates (beats per minute) of Our Class

Today’s Concepts

• Standard Deviation• Box and Whisker Plot

Standard Deviation

• The standard deviation of a data set tells you the average distance a given data value is away from the mean. • This is useful because it gives you an idea of how spread

out your data is!

Standard Deviation

• Can be calculated by the formula:

• Or can be found using the calculator:• STAT → Edit → [enter data values in 1 column]• STAT → Calc → 1-Var Stats → 2nd → LIST → [choose

list you entered data in] → Enter• Your standard deviation is σ

2 2 21 2( ) ( ) ... ( )nx x x x x x

n

Heart Rate Example

• Find the standard deviation of our data set!

Illini Example

• The table below shows the number of points the University of Illinois’ basketball team has put up this season. Find the standard deviation of the data set.

Points Scored by 2012-2013 Fighting Illini Basketball

75 75 89 78 94 84 78 63 75 7285 64 66 73 81 68 74 67 51 75

Box-and-Whisker Plots

• A box-and-whisker plot is constructed by plotting a data set’s 5-number summary:• LV: Lowest Value• Q1: Quartile 1 (separates lowest ¼ from the top ¾)• Q2: Quartile 2 (the median)• Q3: Quartile 4 (separates lowest ¾ from top ¼)• GV: Greatest Value

Constructing a Box-and-Whisker Plot by hand:

• Arrange the data from least to greatest and identify LV and GV

• Find the median of the entire set (Q2)

• Find the median of the first half of the data (Q1)

• Find the median of the second half of the data (Q3)

• Create the box-and-whisker plot

Box-and-Whisker Plots

Illini Example

• The table below shows the number of points the University of Illinois’ basketball team has put up this season. Construct a box-and-whisker plot of the data set.

Points Scored by 2012-2013 Fighting Illini Basketball

75 75 89 78 94 84 78 63 75 7285 64 66 73 81 68 74 67 51 75

Box-and-Whisker Plots

How to get the 5-number summary on a calculator:• Repeat same steps that were used to find standard deviation• LV is given by “minX”• Q1 and Q3 are given by their normal names• Q2 is given by “Med”• GV is given by “maxX”

Heart Rate Example

•Construct a box-and-whisker plot of our data set!

Homework

• pg. 449 #