Chapter-1Introduction and Descriptive

StatisticsDr. Srilakshminarayana.G

Learning Objectives

Difference between cross-sectional data and time-series data

Distinguish between qualitative data and quantitative data.

Describe nominal, ordinal, interval, and ratio scales of measurements.

Different types of charts that describe data sets.

Explain measures of central tendency, dispersion and how to computethem.

Use Excel to create charts and compute various measures.

After studying this chapter, we should be able to:

Statistics is a science that helps us make better decisionsin business and economics as well as in other fields.

Statistics teaches us how to summarize, analyze, anddraw meaningful inferences from data that then lead toimprove decisions.

These decisions that we make help us improve therunning, for example, a department, a company, theentire economy, etc.

What is Statistics?

Using Statistics (Two Categories) Inferential Statistics

Predict and forecast values of population parameters

Test hypotheses about values of population parameters

Make decisions

Descriptive StatisticsCollectOrganizeSummarizeDisplayAnalyze

Cross-Sectional data and Time-Series data

Cross-Sectional data: Data collected at a given point of time or during atime interval.

Examples:

1. Information gathered about the quality of a product from a group ofrespondents involved in a market research.

2. Ratings given by the employees about the facilities provided in theorganization.

3. Closing stock price of 25 stocks collected on 25.06.2014.

4. Information gathered from market regarding the satisfaction levels of thecustomers.

Time series data: Data collected at different time points regarding a characteristicunder study. Data change as the time changes.

Examples

1. Daily, monthly, yearly sales of a product.

2. Gross revenue of an organization taken for the last 10 years.

3. Budget allotment for a sector.

4. Prices of a stock that change with change in time.

5. Petrol prices of a nation that change with time.

6. Production of units that change monthly.

Types of Variables - Two Types Qualitative - Categorical or Nominal:

Examples are-ColorGenderNationality

Quantitative - Measurable or Countable: Examples are-TemperaturesSalariesNumber of points scored on a 100 point exam

Example 1Realtors who help sell condominiums in the Boston area provideprospective buyers with the information given in Table 11.Which of the variables in the table are quantitative and whichare qualitative?

Example-2The election commissioner wants to know the details of the parties andtheir spread over different constituencies. The following table has beengiven to him. Identify the quantitative variables and qualitative variables

S.No Party

Name

Number of

candidates

Zone Number of

Voters

Amount

Spent

1 Party-A 14 A, E, D 1,25,000 2,75,000

2 Party-B 20 B, D, E 1,27,000 2,25,000

3 Party-C 21 A, B, C 2,15,000 2,75,000

4 Party-D 20 D, E, F 2,00,000 2,40,000

5 Party-E 18 A, B, D 1,75,000 2,15,000

6 Party-F 15 D, E, F 1,25,000 2,20,000

7 Party-G 16 F, G, E 1,30,000 2,10,000

Scales of Measurement Nominal Scale - groups or classes

Gender, color, professional classification, etc.

Ordinal Scale - order mattersRanks (top ten videos, products, etc.)

Interval Scale - difference or distance matters has arbitrary zero value.Temperatures (0F, 0C), marks, time,

Ratio Scale - Ratio matters has a natural zero value.Salaries, Sales, costs, market share, number of purchasers, distance

travelled, etc.

Nominal Scale

In the nominal scale of measurement, numbers are used simply as labels forgroups or classes.

If our data set consists of blue, green, and red items, we may designate blue as 1,green as 2, and red as 3. In this case, the numbers 1, 2, and 3 stand only for thecategory to which a data point belongs. Nominal stands for name ofcategory.

The nominal scale of measurement is used for qualitative rather thanquantitative data: blue, green, red; male, female; professional classification;geographic classification; and so on.

Ordinal Scale

In the ordinal scale of measurement, data elements may be ordered

according to their relative size or quality.

Four products ranked by a consumer may be ranked as 1, 2, 3, and 4,

where 4 is the best and 1 is the worst. In this scale of measurement we do

not know how much better one product is than others, only that it is

better.

Interval ScaleIn the interval scale of measurement the value of zero is assigned arbitrarily andtherefore we cannot take ratios of two measurements. But we can take ratios ofintervals. A good example is how we measure time of day, which is in an intervalscale. We cannot say 10:00 A.M. is twice as long as 5:00 A.M. But we can say thatthe interval between 0:00 A.M. (midnight) and 10:00 A.M., which is a duration of10 hours, is twice as long as the interval between 0:00 A.M. and 5:00 A.M., whichis a duration of 5 hours. This is because 0:00 A.M. does not mean absence of anytime. Another example is temperature. When we say 0F, we do not mean zero heat.A temperature of 100F is not twice as hot as 50F.

Ratio Scale

If two measurements are in ratio scale, then we can take ratios of those

measurements. The zero in this scale is an absolute zero. Money, for

example, is measured in a ratio scale. A sum of $100 is twice as large as$50. A sum of $0 means absence of any money and is thus an absolutezero. We have already seen that measurement of duration (but not time ofday) is in a ratio scale. In general, the interval between two interval scalemeasurements will be in ratio scale. Other examples of the ratio scale are

measurements of weight, volume, area, or length.

Example 1The HR manager of an organization wishes to identify employeessatisfaction level with respect to the working conditions of theorganization. The following questionnaire was formulated to get thedetails from the employees. The questionnaire was divided into twosections. The first section includes demographic characteristics ofthe respondents. The other section focus on their satisfaction levelswith respect to different parameters.

1. Age < 20 20-30 30-40 40-50 > 50

2. Experience 15

3. Gender male female

4. Marital status married unmarried

5. Position

6. Department

Questionnaire for the study on employee satisfaction:Kindly fill the questionnaire by giving a tick on the appropriate box for the questions.

Working conditions and hygiene issues

1. Satisfaction with the surrounding environment and general layout of office

2. Satisfaction with the geographically situated workplace

Extremely satisfied

very satisfied

moderately satisfied

slightly satisfied

not at all satisfied

Extremely satisfied

very satisfied

moderately satisfied

slightly satisfied

not at all satisfied

3. Satisfaction of parking facility

4. Satisfaction of canteen facility

Extremely satisfied very satisfied

moderately satisfied

slightly satisfied

not at all satisfied

Extremely satisfied very satisfied

moderately satisfied

slightly satisfied

not at all satisfied

Example-2A survey by an electric company contains questions on the following:1. Age of household head.2. Gender of household head.3. Number of people in household.4. Use of electric heating (yes or no).5. Number of large appliances used daily.6. Average number of hours heating is on.7. Average number of heating days.8. Household income.9. Average monthly electric bill.10. Ranking of this electric company as compared with two previous electricity suppliers.

Example-3

An individual federal tax return form asks, among other things, for the

following information: income (in dollars and cents), number ofdependents, whether filing singly or jointly with a spouse, whether ornot deductions are itemized, amount paid in local taxes. Describe the

scale of measurement of each variable, and state whether the variable is

qualitative or quantitative.

Example-4Describe each of the following variables as qualitative (categorical) orquantitative