BUSINESS STATISTICS

1. What is statistical survey?

Statistical surveys are used to collect quantitative information about items in a population. A survey may focus on opinions or factual information depending on its purpose, and many surveys involve administering questions to individuals. When the questions are administered by a researcher, the survey is called a structured interview or a researcher-administered survey. When the questions are administered by the respondent, the survey is referred to as a questionnaire or a self-administered survey.

2. What are the advantages of survey?

§  Efficient way of collecting information

§  Wide range of information can be collected

§  Easy to administer

§  Cheaper to run

3. What are the disadvantages of survey?

§  Responses may be subjective

§  Motivation may be low to answer

§  Errors due to sampling

§  If the question is not specific, it may lead to vague data.

4. What are the various modes of data collection?

§  Telephone

§  Mail

§  Online surveys

§  Personal survey

§  Mall intercept survey

5. What is sampling?

“Sampling” basically means selecting people/objects from a “population” in order to test the population for something. For example, we might want to find out how people are going to vote at the next election. Obviously we can’t ask everyone in the country, so we ask a sample.

Classification, Tabulation & Presentation of data

1. What are the types of data collection?

Qualitative Data

§  Nominal, Attributable or Categorical data

§  Ordinal or Ranked data

Quantitative or Interval data

§  Discrete data

§  Continuous measurements

2. What is tabulation of data?

Tabulation refers to the systematic arrangement of the information in rows and columns. Rows are the horizontal arrangement. In simple words, tabulation is a layout of figures in rectangular form with appropriate headings to explain different rows and columns. The main purpose of the table is to simplify the presentation and to facilitate comparisons.

3. What is presentation of data?

Descriptive statistics can be illustrated in an understandable fashion by presenting them graphically using statistical and data presentation tools.

4. What are the different elements of tabulation?

Tabulation:

§  Table Number

§  Title

§  Captions and Stubs

§  Headnotes

§  Body

§  Source

5. What are the forms of presentation of the data?

Grouped and ungrouped data may be presented as :

§  Pie Charts

§  Frequency Histograms

§  Frequency Polygons

§  Ogives

§  Boxplots

Measures used to summarise data

1. What are the measures of summarizing data?

§  Measures of Central tendency: Mean, median, mode

§  Measures of Dispersion: Range, Variance, Standard Deviation

2. Define mean, median, and mode?

Mean: The mean value is what we typically call the “average.” You calculate the mean by adding up all of the measurements in a group and then dividing by the number of measurements.

Median: Median is the middle most value in a series when arranged in ascending or descending order

Mode: The most repeated value in a series.

3. Which measure of central tendency is to be used?

The measure to be used differs in different contexts. If your results involve categories instead of continuous numbers, then the best measure of central tendency will probably be the most frequent outcome (the mode). On the other hand, sometimes it is an advantage to have a measure of central tendency that is less sensitive to changes in the extremes of the data.

4. Define range, variance and standard deviation?

The range is defined by the smallest and largest data values in the set.

Variance: The variance (σ²) is a measure of how far each value in the data set is from the mean.

Standard Deviation: it is the square root of the variance.

5. How can standard deviation be used?

The standard deviation has proven to be an extremely useful measure of spread in part because it is mathematically tractable.

 Probablity

1. What is Probability?

Probability is a way of expressing knowledge or belief that an event will occur or has occurred.

2. What is a random experiment?

An experiment is said to be a random experiment, if it’s out-come can’t be predicted with certainty.

3. What is a sample space?

The set of all possible out-comes of an experiment is called the sample space. It is denoted by ‘S’ and its number of elements are n(s).

Example; In throwing a dice, the number that appears at top is any one of 1,2,3,4,5,6. So here:

S ={1,2,3,4,5,6} and n(s) = 6

Similarly in the case of a coin, S={Head,Tail} or {H,T} and n(s)=2.

4. What is an event? What are the different kinds of event?

Event: Every subset of a sample space is an event. It is denoted by ‘E’.

Example: In throwing a dice S={1,2,3,4,5,6}, the appearance of an event number will be the event E={2,4,6}.

Clearly E is a sub set of S.

Simple event: An event, consisting of a single sample point is called a simple event.

Example: In throwing a dice, S={1,2,3,4,5,6}, so each of {1},{2},{3},{4},{5} and {6} are simple events.

Compound event: A subset of the sample space, which has more than on element is called a mixed event.

Example: In throwing a dice, the event of appearing of odd numbers is a compound event, because E={1,3,5} which has ‘3’ elements.

5. What is the definition of probability?

If ‘S’ be the sample space, then the probability of occurrence of an event ‘E’ is defined as:

P(E) = n(E)/N(S) =

number of elements in ‘E’
number of elements in sample space ‘S’

Theoretical Distributions

1. What are theoretical distributions?

Theoretical distributions are based on mathematical formulae and logic. It is used in statistics to define statistics. When empirical and theoretical distributions correspond, you can use the theoretical one to determine probabilities of an outcome, which will lead to inferential statistics.

2. What are the various types of theoretical distributions?

§  Rectangular distribution (or Uniform Distribution)

§  Binomial distribution

§  Normal distribution

3. Define rectangular distribution and binomial distribution?

Rectangular distribution: Distribution in which all possible scores have the same probability of occurrence.

Binomial distribution: Distribution of the frequency of events that can have only two possible outcomes.

4. What is normal distribution?

The normal distribution is a bell-shaped theoretical distribution that predicts the frequency of occurrence of chance events. The probability of an event or a group of events corresponds to the area of the theoretical distribution associated with the event or group of event. The distribution is asymptotic: its line continually approaches but never reaches a specified limit. The curve is symmetrical: half of the total area is to the left and the other half to the right.

5. What is the central limit theorem?

This theorem states that when an infinite number of successive random samples are taken from a population, the sampling distribution of the means of those samples will become approximately normally distributed with mean μ and standard deviation σ/√ N as the same size (N) becomes larger, irrespective of the shape of the population distribution.

Sampling & Sampling Distributions

1. What is sampling distribution?

Suppose that we draw all possible samples of size n from a given population. Suppose further that we compute a statistic (mean, proportion, standard deviation) for each sample. The probability distribution of this statistic is called Sampling Distribution.

2. What is variability of a sampling distribution?

The variability of sampling distribution is measured by its variance or its standard deviation. The variability of a sampling distribution depends on three factors:

§  N: the no. of observations in the population.

§  n: the no. of observations in the sample

§  The way that the random sample is chosen.

3. How to create the sampling distribution of the mean?

Suppose that we draw all possible samples of size n from a population of size N. Suppose further that we compute a mean score for each sample. In this way we create the sampling distribution of the mean.

We know the following. The mean of the population (μ) is equal to the mean of the sampling distribution (μ_x). And the standard error of the sampling distribution (σ_x) is determined by the standard deviation of the population (σ), the population size, and the sample size. These relationships are shown in the equations below:

μ_x = μ   and σ_x = σ * sqrt( 1/n – 1/N )

BUSINESS STATISTICS NOTES