HistogramMost common graph of the

distribution of one quantitative variable

How to make a histogram1. Divide the range of the data into classes

(groups) of equal width and make a frequency table.

2. Label & scale your axes and title your graph.

3. Draw a bar that represents the count in each class (group). The base of the bar should cover its class, and the bar height is the class count.

4. Bars touch each other unless a class is empty.

TipsO There is no one right choice of the classes in a

histogram. Too few will give a “skyscraper” graph. Too few will create a “pancake” graph.

O Five classes is a good minimum.

O Make each class is the same width.

O If you use a computer or graphing calculator, beware of letting the device choose the classes.

O You can add a “break-in-scale” symbol ( // ) on the axis that does not start at 0.

How to describe a Distribution Symmetric – the right and the left sides of

the histogram are approximately mirror images of each other

OSkewed to the right – right side of the histogram extends much farther out than the left side

OSkewed to the left – left side of the histogram extends much farther out than the right side

O Others shapes may appear – ex. clusters, two peaks, unimodal(one peak)

Turn to page 57 and look at 1.11

Relative frequency, cumulative frequency, percentiles, and ogivesOpth percentile of a distribution is

the value such that p percent of the observations fall at or below it.

Example – on Standardized test report – in 80th percentile – means 80% of the people who took the test earned scores that were less or equal to your score. The other 20% of students taking the test earned higher scores than you did.

Relative cumulative frequency graph - ogive

How to construct an ogive1. Decide on class intervals & make a

frequency table, just like histogram.

2. Add three columns to your frequency table:

1. Relative frequency2. Cumulative frequency3. Relative cumulative frequency

O Relative frequency column – Divide the count in each class by the total number of individuals. Convert to percent

O Cumulative frequency column – add the counts in the frequency column that fall in or below the current class interval

O Relative cumulative frequency column – divide the entries in the cumulative frequency column by total number of individuals

3. Label & scale your axes and title your graph.

4. Plot a point corresponding to the relative cumulative frequency in each class interval at the left endpoint of the next class interval.

Example:

Time PlotOA display of change over timeOTime scale – horizontal axisOVariable of interest – vertical axisO If possible connect the points by a line to

help show the pattern of change over time

OLook for a trend – a long-term upwards or downward movement over time.

OSeasonal variation – a pattern that repeats itself at regular time intervals