Standard Deviations with Grouped Data

or

is the frequency of the interval

is the midpoint of the interval

μ or is the mean

p. 148# 7a

5.7 Quartiles and Interquartile Range

When discussing the spread and medians, we break the data into 4 quartiles. First we find the median, which divides the data into two halves. Then we find the median of each half. The median of the bottom half is called and the median of the top half is called . The ranges in between these interesting points are called quartiles.

Ex 1 The results of a survey asking people at a sci-fi convention how many times they've seen Star Wars:

3, 4, 2, 8, 10, 5, 1, 15, 16, 6, 3, 4, 9, 12, 3, 30, 2, 10, 7

(a) Find the median,,.

The Interquartile Range (IQR) is a measure of spread that discusses how data is dispersed about the median. IQR - -. Sometimes the semi-interquartile range is asked for, the equation is .

(b) Find the IQR for the given data.

Box and Whisker Plots

A box and whisker plot is a graph used to display the IQR graphically. First plot the big five points above a number line (ie the big five are: minimum value, , median, , maximum value). Next, you draw a box with at the midpoint of the left side and at the midpoint of the right side. Now, divide the box with a vertical line at the median and connect to the minimum point and to the maximum point with straight lines.

Percentiles

Percentiles are similar to quartiles except they divide the data into 100 intervals with an equal number of data points in them. For example, 40% of the data is less than or equal to the 40^th percentile.

Ex 2 p. 145 example 5

p. 148# 2-4, 6bcd, 7bc, 11, 14