DAY 2 09 Jan 2014

Today is too cold for me.

a. Yes

b. No

Recap: Ø  Statistics => Descriptive & Inferential

Ø  Population & Sample Ø Organizing Data : Variables & Data Ø Data => Qualitative & Quantitative

Objective of the day: Organizing Data

Qualitative Data Quantitative Data

Objective of the day: Organizing Data

Organizing Data into TABLE

56 23 12

11 10 111

Objective of the day: Organizing Data

Organizing Data into Charts

1st Qtr 2nd Qtr 3rd Qtr 4th Qtr

Objective of the day: Organizing Data

Organizing Data into Graphs

0

2

4

6

Organizing Data into Graphs

Section 2.2 Organizing Qualitative Data

Definition

Frequency Distribution of Qualitative Data A frequency distribution of qualitative data is a listing of the distinct values and their frequencies.

Example

Political party affiliations of the students in introductory statistics

Table 2.1

Table for constructing a frequency distribution for the political party affiliation data in Table 2.1

Table 2.2

Definition

Relative-Frequency Distribution of Qualitative Data A relative-frequency distribution of qualitative data is a listing of the distinct values and their relative frequencies.

Relative-Frequency Distribution of Qualitative Data =

Frequency Sample Size

Relative-frequency distribution for the political party affiliation data in Table 2.1

Table 2.3

Example

Pie chart of the political party affiliation data in Table 2.1

Bar chart of the political party affiliation data in Table 2.1

What do you mean by frequency distribution of qualitative data ? A.  A frequency distribution of qualitative data is a listing of

the distinct values and their frequencies.

B.  I don’t know the answer L

Section 2.3 Organizing Quantitative Data

To organize quantitative data, we first group the observations into Classes (which is also called Categories or bins) and then treat the classes as the distinct values of quantitative data.

Once we group the quantitative data into classes, we can construct frequency and relative-frequency distributions of the data in exactly the same way as we did in previous section 2.2.

To group quantitative data we use: 1.  Single-value grouping

2.  Limit grouping

3.  Cut point grouping

Organizing Quantitative Data

Number of TV sets in each of 50 randomly selected households.

1. Single value grouping: In this grouping each class represents a single value and called single valued classes.

Table 2.5

Example:

Frequency and relative-frequency distributions, using single-value grouping, for the number-of-TVs data in Table 2.4

1. Single value grouping:

Days to maturity for 40 short-term investments

2. Limit grouping : In this grouping method each class consists of a range of values.

Table 2.6

Example:

2. Limit grouping

Table 2.7

Frequency and relative-frequency distributions, using limit grouping, for the days-to-maturity data in Table 2.6

Definition Terms Used in Limit Grouping Lower class limit: The smallest value that could go in a class. Upper class limit: The largest value that could go in a class. Class width: The difference between the lower limit of a class and the lower limit of the next-higher class. Class mark: The average of the two class limits of a class.

Definition

Terms Used in Cutpoint Grouping Lower class cutpoint: The smallest value that could go in a class. Upper class cutpoint: The smallest value that could go in the next-higher class (equivalent to the lower cutpoint of the next-higher class). Class width: The difference between the cutpoints of a class. Class midpoint: The average of the two cutpoints of a class.

1.  Single value grouping is particularly suitable for discrete data in which there are only a small number of distinct values.

2.  Limit value grouping is particularly suitable when the data are expressed as a whole numbers and there are too many distinct values to employ single-value grouping.

3.  Cutpoint grouping is useful when the data are continuous and are expressed with decimals.

Things to remember ...

Three common methods for graphically displaying quantitative data:

•  Histogram •  Dotplots •  Stem-and-leaf diagrams

Histogram A histogram displays the classes of the quantitative data on a horizontal axis and the frequencies (relative frequencies, percents) of those classes on a vertical axis. The frequency (relative frequency, percent) of each class is represented by a vertical bar whose height is equal to the frequency (relative frequency, percent) of that class. The bars should be positioned so that they touch each other. •  For single-value grouping, we use the distinct values of the observations to label the bars, with each such value centered under its bar. •  For limit grouping or cutpoint grouping, we use the lower class limits (or, equivalently, lower class cutpoints) to label the bars. Note: Some statisticians and technologies use class marks or class midpoints centered under the bars.

Histogram Single-value grouping. Number of TVs per household: (a) frequency histogram; (b) relative-frequency histogram

Limit grouping. Days to maturity: (a) frequency histogram; (b) relative-frequency histogram

Histogram

Dotplots

Prices, in dollars, of 16 different brands and style of DVD players

Stem-and-leaf diagram

Step 1. Think of each observation as a stem – consisting of all but the right most digit- and a leaf, rightmost leaf. Step 2. Write the stem from smallest to largest in a vertical column to the left of a vertical rule. Step 3. Write each leaf to the right of the vertical rule in the row that contains the appropriate stem. Step 4. Arrange the leaves in each row in ascending order.

Example

Days to maturity for 40 short-term investments

Stem: 7, 6, 9, 5, 4, 8, 3

Stem: 3, 4, 5, 6, 7, 8, 9

Example

Days to maturity for 40 short-term investments

Stems Leaves

Cholesterol levels for 20 high-level patients Stem-and-leaf diagram for cholesterol

levels: (a) one line per stem; (b) two lines per stem

Example

Summary

Ø Organizing data => Qualitative and Quantitative.

Ø To group quantitative data => single-value, limit, cutpoint

Ø Histogram, Dotplots, Stem-and-leaf

Next Week...

1. Sections 2.4, 3.1, 3.2 2. Lab: Section 2.3 & Quiz 1 (1.1-2.3) 3. Sections 3.3 & 3.4

Thank You J