Question

In your own words, Differentiate the following statistical terminology with some examples.

a. Population parameter and Sample Statistic.

b. Descriptive Statistic and inferential Statistic.

C. Nominal Scale and Ordinal Scale

d. Primary Data Source and Secondary Data Sources.

2. Data showing the population by state in million of people follow ( The World Almanac, 2012) The dataset in Excel file 2012Population.XLsx.

a. Develop a frequency distribution, a percent frequency distribution, and a histogram Use a class width of 2.5 million.

b. Does there appear to be any skewness in the distribution? Explain

c. What observation can you nake about the population of the 50 states?

Answer 1

Answers:

Que 1)

Ans a)

Population Parameters versus Sample Statistics:

A parameter is a value that describes a characteristic of an entire population, such as the population mean. Because you can almost never measure an entire population, you usually don’t know the real value of a parameter. In fact, parameter values are nearly always unknowable. While we don’t know the value, it definitely exists.

For example, the average height of adult women in the United States is a parameter that has an exact value—we just don’t know what it is!

The population means and standard deviation are two common parameters. In statistics, Greek symbols usually represent population parameters, such as μ (mu) for the mean and σ (sigma) for the standard deviation.

A statistic is a characteristic of a sample. If you collect a sample and calculate the mean and standard deviation, these are sample statistics. Inferential statistics allow you to use sample statistics to make conclusions about a population. However, to draw valid conclusions, you must use particular sampling techniques. These techniques help ensure that samples produce unbiased estimates.

Ans b)

Difference between Descriptive and Inferential Statistics:

Although descriptive statistics are helpful in learning things such as the spread and center of the data, nothing in descriptive statistics can be used to make any generalizations. In descriptive statistics, measurements such as the mean and standard deviation are stated as exact numbers.

Even though inferential statistics uses some similar calculations — such as the mean and standard deviation — the focus is different for inferential statistics. Inferential statistics start with a sample and then generalize to a population. This information about a population is not stated as a number. Instead, scientists express these parameters as a range of potential numbers, along with a degree of confidence.

Ans c)

Nominal Scale:

Nominal Scale, also called the categorical variable scale, is defined as a scale used for labeling variables into distinct classifications and doesn’t involve a quantitative value or order. This scale is the simplest of the four variable measurement scales. Calculations done on these variables will be futile as there is no numerical value of the options.

There are cases where this scale is used for the purpose of classification – the numbers associated with variables of this scale are only tags for categorization or division. Calculations done on these numbers will be futile as they have no quantitative significance.e.g.

Where do you live?

• 1- Suburbs
• 2- City
• 3- Town

The nominal scale is often used in research surveys and questionnaires where only variable labels hold significance.

Ordinal scale:

Ordinal Scale is defined as a variable measurement scale used to simply depict the order of variables and not the difference between each of the variables. These scales are generally used to depict non-mathematical ideas such as frequency, satisfaction, happiness, a degree of pain, etc. It is quite straightforward to remember the implementation of this scale as ‘Ordinal’ sounds similar to ‘Order’, which is exactly the purpose of this scale.

Ordinal Scale Examples

Status at the workplace, tournament team rankings, the order of product quality, and order of agreement or satisfaction are some of the most common examples of the Ordinal Scale. These scales are generally used in market research to gather and evaluate relative feedback about product satisfaction, changing perceptions with product upgrades, etc.

Ans d)

Primary data

An advantage of using primary data is that researchers are collecting information for the specific purposes of their study. In essence, the questions the researchers ask are tailored to elicit the data that will help them with their study. Researchers collect the data themselves, using surveys, interviews, and direct observations.

Secondary data

There are several types of secondary data. They can include information from the national population census and other government information collected by Statistics Canada. One type of secondary data that’s used increasingly is administrative data. This term refers to data that is collected routinely as part of the day-to-day operations of an organization, institution, or agency. There is any number of examples: motor vehicle registrations, hospital intake and discharge records, workers’ compensation claims records, and more.