1. Section 2.3 Measures of Center and Spread

2.  1) What were the main topics of 2.3?  2) What are the measures of center?  3) What is an IQR?  4) What are the values of a 5-Number Summary?  5) How do you determine if a value is truly considered an outlier?

3.  Mean (average):  Sum of x’s / total number of values  It is the balance point of a distribution  Median is the value the divides the data into 2 halves.  The middle number or average of middle 2 numbers.  1,3,6,8,9 Median is 6  1,3,7,9,10,15 Median is (7+9)/2=8

4.  An extreme outlier has a larger effect on the mean than the median. Why?  1,4,6,8 Find the mean and median  1,4,6,8 and 55: Now find the mean and median  Remember the mean is the balance point of a distribution and the median is the middle number.

5.  Use the Speed of Mammals to investigate median and the 5-Number Summary:  Find the median of the Predators: Find the lower or first quartile of the Predators: (omit the median) Find the upper of third quartile of the Predators: (omit the median) What are the minimum and maximum values for Predators: The 5-Number Summary and gives a measure of center and spread. Now do the same for the non-predators:

6.  Use the 5-Number Summary to create a box and whisker plot.  When comparing two groups use the same scale and place box and whisker plots on top of each other.  Use the mammal speed data to compare wild mammals to non-wild mammals with box and whisker plots.

7.  Page 63 D16  Page 69 P16, 18, 19, 21

8.  The IQR is a measure of the spread of the middle 50% of the data.  IQR=Q3-Q1  This can be use to determine if a value is an outlier.  If the value is more than 1.5 times the IQR from the nearest quartile.  Outliers in a Boxplot.

9.  Measuring Hand Span Activity  Using a ruler, measure your hand span to the nearest mm.  Write your result on the board.  Enter all data into calculator.  Find the 5 Number Summary of the data. ▪ (1-var stats) ▪ Create a box plot  Enter L1-mean into L2  Use 1-var stats to find the sum of this:

10.  Think about what subtracting the mean (x) from your data values does.  It tells how far your hand span is from the class average. ▪ + and your hand span is larger ▪ - and your hand span is smaller  Now think about what summing all of your differences does. What was the result?  Differences from the mean will always sum to be Zero.

11.  Rapid Fire Example, Rapid Fire 2 Rapid Fire ExampleRapid Fire 2  A measure of the average difference from the mean gives you a kind of level of consistency.  Think of a target in an archery contest. If you wanted to measure someone’s accuracy, how would you suggest doing it?

13.  The standard deviation of a data set is typically used when the data is roughly normally distributed.  It measures the “average” distance from the mean.  This is a measure of spread. (how far are the arrows spread apart)  To calculate a SD, we must figure out a way to find the average difference from the mean, but we know that the sum of the differences is always = zero.  So we square the difference, then sum that, then divide to find average sum of squares, then take the square root.

14.  The SD squared: (s 2 ) is called the variance.  It is not used as often, but is important to know what it is, in case it is a piece of information given.

15.  You can get the SD from the calculator.  Sx is the SD of a sample of data.  σx is the SD of an entire population (we will discuss the difference later)  Note the other sums and values you can get.  Σx will give the sum of you list of values  Σx 2 will give the sum of squared values  n is your total number of data values in the list  Then is your 5-Number Summary

16.  Frequency Tables show the values and the frequency that they occur in the data set.  You can easily find the mean of this data:  You can find the SD:  It is easy to find with Calculator:  L1:x values, L2: frequencies, 1-var stat L1,L2

17.  Page 70 P22-P25

18.  Page 71: E29, 31, 33, 35, 37, 38, 43