Chapter 1: Exploring DataSec. 1.2: Displaying Quantitative Data with Graphs, cont.

HistogramsHistogram - a graph of the distribution of one quantitative variable where nearby values are grouped together.

How to make a histogram:

1) Divide the range of data into classes of equal width.

2) Find the count (frequency) or percent (relative frequency) of individuals in each class.

3) Label and scale your axes and draw the histogram. The height of the bar equals its frequency. Adjacent bars should touch, unless a class contains no individuals.

Example, p. 33 - 34

This table presents data on the percent of residents from each state who were born outside of the U.S.

Start by deciding on a width for each class:• Identify the smallest and largest values.

• Think of a range that contains both.

0 - 30• Pick a number that

divides the range evenly.

5

Example, p. 33 - 34

This table presents data on the percent of residents from each state who were born outside of the U.S.

Next, make a frequency table:

Frequency Table

Class Count

Total

0 to < 55 to < 1010 to <

1515 to < 2020 to < 2525 to < 30

20

13

9

5

2

1

50

Example, p. 33 - 34Next, make a histogram:

Frequency Table

Class Count

Total

0 to < 55 to < 1010 to <

1515 to < 2020 to < 2525 to < 30

20

13

9

5

2

1

50

Percent of foreign-born residents

Num

ber

of

Sta

tes 0 5 10 15 20 25 30

20

18

16

14

12

10

8

6

4

2

0

Count vs. Percent

Describing HistogramsShape – skewed right and unimodal.

Outliers – No obvious observations outside the overall pattern.

Center – Would fall somewhere between 5 to 9.9%.

Spread – Varies from less than 5% to over 25%. (Could also go back to original data: 1.2% to 27.2%)

Example on p. 35

***Same example as before, but they’ve changed the class width to be 2.5.***

Using Histograms Wisely

Here are several cautions based on common mistakes students make when using histograms.

Cautions!

1) Don’t confuse histograms and bar graphs.

2) Don’t use counts (in a frequency table) or percents (in a relative frequency table) as data.

3) Use percents instead of counts on the vertical axis when comparing distributions with different numbers of observations.

4) Just because a graph looks nice, it’s not necessarily a meaningful display of data.

Histograms on the TI-calculator

Push STAT. Push ENTER.

Histograms on the TI-calculator

9 66 78 96 48 38 46 5

6.5 65 6

11 63 66 107 8

4.5 97 7 Enter data. (All in the L1

column.) After you have entered one

observation, press ENTER to go to the next line.

Push 2nd and QUIT (MODE). Press 2nd STAT PLOT (Y=).

Histograms on the TI-calculator

Push ENTER. Make sure Plot 1 is On –

Highlight On and press ENTER.

Select the Histogram under Type.

Make sure your Xlist matches the list you entered your data.

Push GRAPH. For a better picture, press

ZOOM 9:ZoomStat.

Histograms on the TI-calculator

Push TRACE. This allows you to see what

the range is for each class and the number that fall in that class.

If you want to change the class width:

• Press WINDOW and change settings.

Histograms on the HP Prime

9 66 78 96 48 38 46 5

6.5 65 6

11 63 66 107 8

4.5 97 7 Push Apps.

Highlight or press Statistics 1 Var

Enter data.

Histograms on the HP Prime

Push Plot. To Zoom in, Press Menu

Press Zoom Select 3 In

Histograms on the HP Prime

To change window, push 2nd, Plot.

Push Plot.

Histograms on the HP Prime

If you want to Trace, press Menu and check to see that there is a dot beside Trace.

Press Menu again.

The Practice of Statistics, 5th Edition 17

MAKE and INTERPRET dotplots and stemplots of quantitative

data

DESCRIBE the overall pattern of a distribution

IDENTIFY the shape of a distribution

MAKE and INTERPRET histograms of quantitative data

COMPARE distributions of quantitative data

Data Analysis: Making Sense of Data

Homework – Due Monday P. 44 – 45 #52 & 57