chapter 1.4. variable: any characteristic whose value may change from one individual to another...

Chapter 1.4

Variable:

• any characteristic whose value may change from one individual to another

Data:

• observations on single variable or simultaneously on two or more variables

Types of variables

Categorical variables

• or qualitative

• identifies basic differentiating characteristics of the population

Numerical variables• or quantitative

• observations or measurements take on numerical values

• makes sense to average these values

• two types - discrete & continuous

Classification by the number of variables

• Univariate - data that describes a single characteristic of the population

• Bivariate - data that describes two characteristics of the population

• Multivariate - data that describes more than two characteristics (beyond the scope of this course

Identify the following:

• gender• age• hair color• smoker • systolic blood

pressure• number of girls in

class

• categorical• numerical• categorical• categorical• numerical• numerical

Categorical Data

Frequency

• the number of times the category appears in the data set

Frequency Distribution

• a table that displays the possible categories along with the associated frequencies or relative frequencies

Relative Frequency• The fraction or proportion of

the time that the category appears in the data set;

frequency

# of observations in the data set

Relative Frequency

• percent displayed as a decimal

Relative Frequency Distribution

• a table that includes relative frequencies

Table 4. Life of AA batteries, in minutes

Battery life, minutes (x)

Frequency (f)Relative frequency

Percent frequency

360–369 2 0.07 7

370–379 3 0.10 10

380–389 5 0.17 17

390–399 7 0.23 23

400–409 5 0.17 17

410–419 4 0.13 13

420–429 3 0.10 10

430–439 1 0.03 3

Total 30 1.00 100

Life of AA batteries, in minutes

Bar Graphs• Provides a visual representation

of the information from a frequency distribution where the area of each bar is proportional to the corresponding frequency

• Look for frequently and infrequently occurring categories

BAR GRAPHS

• Step 1: Label your axes of the graph. Draw a set of axes. Label you horizontal axis with your type that your categories fit in to. Title your graph.

• Step 2: Scale your axes. Use the counts in each category to help you scale your vertical axis. Write the category names at equally spaced intervals beneath the horizontal axis.

• Step 3: Draw a vertical bar above each category name to a height that corresponds to the count in each category.

Numerical Data

Discrete (numerical)

• listable set of values

• usually counts of items

Continuous (numerical)

• data can take on any values in the domain of the variable

• usually measurements of something

DOT PLOT• Use for small data sets• Each observation is

represented by a dot; dots are stacked vertically

• Look for: spread of data, nature of distribution of data, unusual data values

DOT PLOTS• Step 1: Label your axis and title your

graph. Draw a horizontal line and label it with the variable. Title your graph

• Step 2: Scale the axis based on the values of the variable

• Step 3:Mark a dot above the number on the horizontal axis corresponding to each data value.

The number of goals scored by each team in the first round of the California Southern Section Division V high school

soccer playoffs is shown in the following table.

5 0 1 0 7 2 1 0 40 3 0 2 0 3 1 5 0 3 0 1 0 1 0 2 0 3