Lesson 1.1 Day #2Histograms, Ogives, and Timeplots!

Making and interpreting stemplots can be tedious for large data sets. For larger amounts of data, ___________ are the most common way to display the distribution of a ___________variable. The disadvantage of a histogram is that you ___________________.

Displaying Quantitative Variables: Histograms

Histograms

Quantitativelose individual values

Histograms

Divide data into classes of equal width such that each data point falls into only one class.

There is no single correct choice for the number of classes. FIVE is usually a good minimum.

Prepare a frequency table by counting the number of observations in each class.

Tips:

Number and Label your axes and Title your graph.

Draw a bar to represent the count in each class. Remember, NO SPACES between bars (unless the count for that class is ___).

Tips:

0

How many children are in your family?

Histograms

# children

frequency

1 4

2 5

3 6

4 2

5 0

6 1

Fre

qu

en

cy

# of children in family1 2 3 4 5 6

How Many Children?

How tall are you in inches?

Histograms

Height (in)

frequency

56 - 60

61 - 65

66 - 70

71 - 75

76 - 80 Fre

qu

en

cy

Height in inches60 65 70 75 80

Height of Statistics AP Class

How tall are you in inches?

Histograms

Height (in)

frequency

56 x

60 x

65 x

70 x

75 x Fre

qu

en

cy

Height in inches

56 x 61 x 66 x 71 x 76 x

Height of Statistics AP Class

Shape – Unimodal? Bimodal? Symmetric? Skewed? What Direction?

Center – estimate the median…about where would you find the middle value?

Spread – What is the range? Outliers – Do any values seem too far outside the expected range?

ALWAYS Discuss what you see:

When you describe the shape of a distribution, concentrate on the main features. Distributions with a single peak (___________) can be described as

Symmetric –  

  Skewed right –

  Skewed left –

Shape!

UNIMODAL

Of course, not all distributions will be unimodal. A distribution could have two peaks (__________), or show no real peaks (___________).

Shape!

BIMODALUNIFORM

Histograms can be made using the STAT PLOT feature on your calculator (see p. 59).

Be sure to set your own WINDOW - Do not ONLY use the ZOOM STAT feature of your calculator!

On your Calculator

Make a histogram of the salary data in your calculator. BE SURE TO SET THE WINDOW APPROPRIATELY! Draw the histogram in your notes.

Practice

Example: The data* below shows the median starting salary of college graduates with Bachelors Degrees in various fields. Create an appropriate graphical display and describe what you see.

Chemical Engineering $65,700Electrical Engineering $60,200Computer Science $56,400Economics $50,200Statistics $48,600Environmental Science $43,300Business Administration $43,300Political Science $41,300

From www.payscale.com/best-colleges/degrees.asp

July, 2009

Philosophy $40,000Biology $40,000Communications $38,700Fashion Design $36,700Journalism $36,300Education $36,200Graphic Design $36,000Psychology $36,000Social Work $33,400

One more thing about histograms

• Frequency histogram Relative frequency histogram

1 2 3 4 5 60

1

2

3

4

5

6

7

# of children

1 2 3 4 5 60

5

10

15

20

25

30

35

# of children

Fre

qu

en

cy

# of children in family

Re

lati

ve

Fre

qu

en

cy

# of children in family

A histogram does not always tell us everything we want to know about a distribution. Sometimes we want to describe the relative position of an individual within a distribution. For this we use a relative cumulative frequency plot (Ogive).

The pth percentile of a distribution is the value such that p percent of the observations fall at or below it.

Relative Cumulative Frequency Plots (Ogives)

Suppose we want to know the percentile of Statistics majors. In other words, we want to know what percent of majors make the same or less money than Stats majors.

Start with the frequency table and add two columns, Cumulative Frequency and Relative Cumulative Freq:

Interval Frequency

Cum Freq.

Rel. Cum. Freq.

30 < $ < 35

1 1 .06

35 < $ < 40

6 7 .41

40 < $ < 45

5 12 .71

45 < $ < 50

1 13 .76

50 < $ < 55

1 14 .82

55 < $ < 60

1 15 .88

60 < $ < 65

1 16 .94

65 < $ < 70

1 17 1.00

Now, construct a plot with the x-coordinates being the upper end of each class and the y-coordinates being the cumulative frequency.

Interval RCF30 < $ <

35.06

35 < $ < 40

.41

40 < $ < 45

.71

45 < $ < 50

.76

50 < $ < 55

.82

55 < $ < 60

.88

60 < $ < 65

.94

65 < $ < 70

1.00

Ogives

a) In what percentile is a Statistician’s salary?    b) Find the center of the distribution. What degree earns a salary closest to the center?

Time Plots show how a variable changes with time. The time scale goes on the horizontal axis. The variable of interest goes on the vertical axis.

Look for trends (long-term upward or downward movement) and seasonal variations.

Time Plots

Look for trends (long-term upward or downward movement) and seasonal variations.

Time Plots

Look for trends (long-term upward or downward movement) and seasonal variations.

Time Plots