2.2Organizing Quantitative

Data

DataO Consider the following data

O We would like to compute the frequencies and the relative frequencies

Show the Frequency and Rel. Frequency

Number

Tally Freq. Rel. Freq.

1

2

3

4

5

6

7

8

9

10

11

HistogramO Discrete quantitative data can be

presented in bar graphs in several of the same ways as qualitative data

O We use the discrete values instead of the category names

O We arrange the values in ascending order

O For discrete data, these are called histograms

Histograms

OExample of histograms for discrete dataO FrequenciesO Relative frequencies

OUse calculatorO Enter values from table into a listO Plot values and change to

histogram

Histogram – Discrete Data

Calculator PracticeO Making a histogram

ClassesO Continuous data cannot be put directly

into frequency tables since they do not have any obvious categories

O Categories are created using classes, or intervals of numbers

O The continuous data is then put into the classes

ClassesO For ages of adults, a possible set of

classes is20 – 2930 – 3940 – 4950 – 59

60 and olderO For the class 30 – 39

O 30 is the lower class limitO 39 is the upper class limit

Class Width● The class width is the difference between

the upper class limit and the lower class limit

● For the class 30 – 39, the class width is40 – 30 = 10

● Why isn’t the class width 39 – 30 = 9? The class 30 – 39 years old actually is 30 years

to 39 years 364 days old … or 30 years to just less than 40 years old

The class width is 10 years, all adults in their 30’s

Open Ended Classes● All the classes (20 – 29, 30 – 39, 40 –

49, 50 – 59) all have the same widths, except for the last class

● The class “60 and above” is an open-ended class because it has no upper limit

● Classes with no lower limits are also called open-ended classes

O The classes and the number of values in each can be put into a frequency table

O How many people are between 30 and 39 years old?

Age Number

20 – 29 533

30 – 39 1147

40 – 49 1090

50 – 59 493

60 and older 110

Histogram – continuous data

Stem-and-Leaf Plot● A stem-and-leaf plot is a different way to

represent data that is similar to a histogram

● To draw a stem-and-leaf plot, each data value must be broken up into two components The stem consists of all the digits except for

the right most one The leaf consists of the right most digit For the number 173, for example, the stem

would be “17” and the leaf would be “3”

Stem-and-Leaf Plots● Modifications to stem-and-leaf plots

Sometimes there are too many values with the same stem … we would need to split the stems (such as having 10-14 in one stem and 15-19 in another)

If we wanted to compare two sets of data, we could draw two stem-and-leaf plots using the same stem, with leaves going left (for one set of data) and right (for the other set)

Create a Stem-and-leaf plot

O Birth DATE for students in this class

Dot PlotO A dot plot is a graph where a dot is placed

over the observation each time it is observed

O Not extremely useful but help give us a quick view of distribution

O Make a Dot Plot with the Birthday MONTH

Distribution ShapeO A useful way to describe a variable is by

the shape of its distributionO Some common distribution shapes are

O UniformO Bell-shaped (or normal)O Skewed rightO Skewed left

UniformOA variable has a uniform distribution

whenO Each of the values tends to occur with

the same frequencyO The histogram looks flat

Bell-ShapedOA variable has a bell-shaped

distribution whenO Most of the values fall in the middleO The frequencies tail off to the left and to

the rightO It is symmetric

Skewed RightOA variable has a skewed right

distribution whenO The distribution is not symmetricO The tail to the right is longer than the

tail to the leftO The arrow from the middle to the long tail

points right

Skewed LeftOA variable has a skewed left

distribution whenO The distribution is not symmetricO The tail to the left is longer than the tail

to the rightO The arrow from the middle to the long tail

points left

Identify the Shape of the Following

Time-Series GraphO The following is an example of a

time-series graphO The horizontal axis shows the

passage of time