Homework Questions

Measures of Center and Spread

Unit 5, Statistics

Mean

The mean is more commonly known as the average.

Represented by A six-month study of a busy intersection

reports that the number of accidents per month as 3, 8, 5, 6, 6, 10. Find the mean.

x

Example 2

In the real estate section of the Sunday paper, the following house prices were listed. Find the mean.

$98,000

$136,700

$210,000

$289,900

$315,500

$2,456,500

Median

If the distribution is skewed, or contains extreme values, often the median is the best measure of center.

It is the middle value of your data.3, 4, 7, 8, 9, 11, 15

17, 22, 24, 30, 35, 40

Go back to home prices and find the median instead of the mean…

$98,000

$136,700

$210,000

$289,900

$315,500

$2,456,500

Mode

The mode is the data value that has the highest frequency, which means it occurs the most often in the list of data.

NOTE: if every value in the data occurs the same number of times there is no mode. If two or more repeat the same number of times the set is bimodal (2 values), trimodal (3 values), or multimodal.

Find the mode

Recall the shapes…

For a symmetric distribution, the mean and median are equal

Recall the shapes…

For a distribution skewed to the right, the mean is to the right of the median

Recall the shapes…

For a distribution skewed to the left, the mean is to the left of the median.

Standard Deviation

I am not going to teach you how to find this by hand, but you do need to know what it is…

The Standard Deviation is the most common measure of variability (the spread of the data) and is best used when data is symmetric.

It measures the average distance of a piece of data to the mean.

CALCULATOR TIME!!

Type this into L1 on your calc and find:

= Med = Mode = Standard Deviation =

x

Your turn…

85, 91, 99, 101, 105, 109, 111, 119, 125 =Med =Mode =Standard Deviation =

x

Range

The range is the difference between the maximum and minimum data values.

85, 91, 99, 101, 105, 109, 111, 119, 125Range is 125 – 85 = 40

Interquartile Range

Example: 5, 8, 4, 4, 6, 3, 8 Put them in order: 3, 4, 4, 5, 6, 8, 8

Half way is the Q2

Half of the 1st half is Q1

Half of the 2nd half is Q3

IQR = Q3 - Q1

Find the IQR and the 5 Number Summary

Five Number Summary – Minimum, Q1, Median, Q3, Maximum

1, 3, 3, 4, 5, 6, 6, 7, 8, 8

Box Plot

You can use the 5 Number Summary to create a box plot of the data.

Your turn…

Find the 5 number summary, IQR, and create a box plot of the data

85, 91, 99, 101, 105, 109, 111, 119, 125

Homework

Section 13.2 Worksheet