BUSINESS STATS PRELIMS EXAM

MODULE 1 AND 2

STATISTICS

plural sense: numerical facts, e.g. CPI, peso-dollar exchange rate

STATISTICS

singular sense - scientific discipline consisting of theory and methods for processing numerical information that one can use when making decisions in the face of uncertainty.

DESCRIPTIVE STATISTICS
INFERENTIAL STATISTICS

2 AREAS OF STATISTICS

DESCRIPTIVE STATISTICS

methods concerned with collecting, describing, and analyzing a set of data without drawing conclusions (or inferences) about a large group.

DESCRIPTIVE STATISTICS

is used to describe a set of data in terms of its frequency of occurrence, its central tendency, and its dispersion.

INFERENTIAL STATISTICS

methods concerned with the analysis of a subset of data leading to predictions or inferences about the entire set of data

INFERENTIAL STATISTICS

It addresses the problem of making broader generalizations or inferences from sample data to population.

POPULATION

it is the totality of all elements or entitles from which the information are obtained.

SAMPLE

It’s the finite number of objects selected from the population. It is a subset of a population

PARAMETER

any numerical measure or value that describes a characteristic or an aspect of a population.

STATISTIC

any numerical measure or value that describes a characteristic or an aspect of a sample.

CENSUS

— a process of collecting information from the population. It also refers to an official count by a national government of the country’s population.

CENSUS

Governments use — information for public policies such as fund allocations for schools and road constructions.

SURVEY

a process of collecting information from a sample.

SURVEY

Generally conducted when the population is too large and getting information from the whole population is costly and time-consuming task.

VARIABLE

any characteristic or information measurable or observable in every element of the population or sample.

QUALITATIVE (CATEGORICAL) VARIABLES
QUANTITATIVE VARIABLES

TYPES OF VARIABLES

QUANTITATIVE VARIABLES

a variable that indicates how much or how many of a characteristic an individual, object, or event possesses. ex. volume, temperature, student grade, score in a quiz, height

QUALITATIVE VARIABLES

a variable that indicates what kind of a characteristic an individual, object, or event possesses. ex. color of cars, juice, favorite basketball team, economic status, student number

DICRETE VARIABLE

a quantitative variable that can assume only countable number of distinct values such as 0, 1, 2, 3, … ex. Number of students in a class, age as used in insurance, point-grade

CONTINUOUS VARIABLE

a variable that can assume infinitely many values corresponding to the points on a line interval. ex. weight, area, time, temperature

NOMINAL LEVEL
ORDINAL LEVEL
INTERNAL LEVEL
RATIO LEVEL

LEVELS OF MEASUREMENT

NOMINAL LEVEL

level of measurement is characterized by data that consists of names, labels, or categories only. The data cannot be arranged in an ordering scheme. ex. gender, civil status, blood type, food preference, etc.

ORDINAL LEVEL

level of measurement involves data that may be arranged in some order, but differences between data values either cannot be determined or are meaningless. ex. nutrition status; level of consciousness; nurses' rank

INTERNAL LEVEL

level of measurement is like the ordinal level, with the additional property that meaningful amounts of differences between data can be determined. However, there are no inherent (natural) zero starting point. ex. body temperature, year (1955, 1776, 1123, etc.)

RATIO LEVEL

level of measurement is the interval modified to include the inherent zero starting point. For values at this level, differences and ratios are meaningful. ex. participants' age, height ,weight, fluid intake, etc.

PRIMARY DATA

is collected from the first-hand experience and is not used in the past. The data gathered by primary data collection methods are specific to the motive of the research, and highly authentic and accurate.

SECONDARY DATA

is the data that has been used in the past. The researcher can obtain data from the sources both internal and external to the organization.

TIME SERIES ANALYSIS
SMOOTHING TECHNIQUES
BAROMETRIC METHOD

STATISTICAL METHODS

TIME SERIES ANALYSIS

refers to a sequential order of values of a variable, known as a trend, at equal time intervals. Using trends, an organization can predict the demand for its products and services for the projected time.

SMOOTHING TECHNIQUES

In cases where the time series lacks significant trends, smoothing techniques can be used. are used to eliminate a random variation from the historical demand. This helps in identifying patterns and demand levels that can be used to estimate future demand. The most common methods used in this technique of demand forecasting are simple moving average method and weighted moving average method.

BAROMETRIC METHOD

Also known as the leading indicators approach, this method is used to speculate future trends based on current developments. When a past event is considered to predict the future event, the past event would act as a leading indicator.

SURVEYS

POLLS

INTERVIEWS
DELPHI TECHNIQUE
FOCUS GROUPS
QUESTIONNAIRE

KINDS OF PRIMARY DATA

SURVEYS

are used to collect data from the target audience and gather insights into their preferences, opinions, choices, and feedback related to their products and services.

POLLS

comprise of one single or multiple choice question. When it is required to have a quick pulse of the audience's sentiments, you can go for polls. Because they are short in length, it is easier to get responses from the people. Can be embedded into various platforms. Once the respondents answer the question, they can also be shown how do they stand as compared to the responses of others.

INTERVIEWS

In this method, the interviewer asks questions either face-to-face or through telephone to the respondents. In face-to-face interviews, the interviewer asks a series of questions to the interviewee in person and notes down responses. In case it is not feasible to meet the person, the interviewer can go for a telephonic interview. This form of data collection is suitable when there are only a few respondents. It is too time-consuming and tedious to repeat the same process if there are many participants.

DELPHI TECHNIQUE

In this method, market experts are provided With the estimates and assumptions of forecasts made by other experts in the industry. Experts may reconsider and revise their own estimates and assumptions based on the information provided by other experts. The consensus of all experts on demand forecasts constitutes the final demand forecast.

FOCUS GROUPS

A small group of people, around 8-10 members come together to discuss the common areas of the problem. Each individual provides his insights on the issue concerned. A moderator regulates the discussion among the group members. At the end of the discussion, the group reaches a consensus.

QUESTIONNAIRE

is a printed set of questions, either open-ended or closed-ended, which the respondents are required to answer on the basis of their knowledge and experience with the issue concerned. is a part of survey, whereas the end-goal of a questionnaire may or may not be a survey.

Statistical Methods

Surveys

Polls

Interview

Delphi Technique

Focus Groups

PRIMARY DATA COLLECTION METHODS

• Financial Reports

• Sales Reports

• Government Reports

• Mission

• Vision Statement

• Internet

SECONDARY DATA COLLECTION METHODS

PRESENTATION OF DATA

— This refers to the organization of data into tables, graphs or charts, paragraph form so that logical and statistical conclusion can be derived from the collected measurements. — Data may be presented in: Tabular, Textual and Graphical

Measures of Central Tendency

— A single value that is used to identify the "center" of the data

— it is thought of as a typical value of the distribution

— precise yet simple

— most representative value of the data

Mean

• Most common measure of the center

• Also known as arithmetic average

Properties of the Mean

Median

Divides the observations into two equal parts:

• If the number of observations is odd, the median is the middle number.

• If the number of observations is even, the median is the average of the 2 middle numbers.

Sample median

denoted as x̃

population median

is denoted as

MODE

— occurs more frequently

— nominal average

— may or may not exist

— can be used for qualitative as well as quantitative data — may not be unique — not affected by extreme values — can be computed for ungrouped and grouped data

Properties of a Mode

sampling stability is desired

other measures are to be computed

Use the mean when:

• the exact midpoint of the distribution is desired

• there are extreme observations

Use the median when:

• when the "typical" value is desired

• when the dataset is measured on a nominal scale

Use the mode when:

Measures of Location

summarizes a data set by giving a value within the range of the data values that describes its location relative to the entire data set arranged according to magnitude (called an array).

Minimum

is the smallest value in the data set, denoted as MIN.

Maximum

is the largest value in the data set, denoted as MAX.

Percentiles

• Numerical measures that give the relative position Of a data value relative to the entire data set.

• Divide an array (raw data arranged in increasing or decreasing order of magnitude) into 100 equal parts.

• The jth percentile, denoted as Pp is the data value in the the data set that separates the bottom j% Of the data from the top (100-j)%.

Percentiles

IS AN EXAMPLE OF —- : Suppose LJ was told that relative to the other scores on a certain test, his score was the 95th percentile. This means that (at least) 95% of those who took the test had scores less that equal to LJ’s score, while (at least) 5% had scores higher than LJ’s.

Deciles

• Divide an array into ten equal parts, each part having ten percent of the distribution of the data values, denoted by Dj.

• The 1st decile is the 10th percentile; the 2nd decile is the 20th percentile.

Quartiles

• Divide an array into four equal parts, each part having 25% of the distribution of the data values, denoted by Q j.

• The 1st quartile is the 25th percentile; the 2nd quartile is the 50th percentile, also the median and the 3rd quartile is the 75th percentile.

Measures of Variation

is a single value that is used to describe the spread of the distribution

measure of central tendency

alone does not uniquely describe a distribution

Absolute Measures of Dispersion
Relative Measure of Dispersion

Two Types of Measures of Dispersion

• Range

• Inter-quartile Range

• Variance

• Standard Deviation

Absolute Measures of Dispersion:

Coefficient of Variation

Relative Measure of Dispersion:

RANGE

the difference between the maximum and minimum value in a data set

💡 R = MAX - MIN

• The larger the value of the range, the more dispersed the observations are.

• It is quick and easy to understand.

• A rough measure of dispersion.

Some Properties of the Range

INTER-QUARTILE RANGE

IQR meaning

INTER-QUARTILE RANGE (IQR)

the difference between the third quartile and first quartile.

Reduces the influence of extreme values.

Not as easy to calculate as the Range.

Some Properties of IQR

VARIANCE

important measure of variation, shows variation about the mean

STANDARD DEVIATION

SD meaning

STANDARD DEVIATION (SD)

most important measure of variation, square root of Variance, has the same units as the original data.

Remarks on Standard Deviation

If there is a large amount of variation, then on average, the data values will be far from the mean. Hence, the SD will be large.

If there is only a small amount of variation, then on average, the data values will be close to the mean. Hence, the SD will be small.

Properties of Standard Deviation

• It is the most widely used measure of dispersion. (Chebychev's Inequality)

• It is based on all the items and is rigidly defined.

• It is used to test the reliability of measures calculated from samples.

• The standard deviation is sensitive to the presence of extreme values.

• It is not easy to calculate by hand (unlike the range).

Coefficient of Variation

CV Meaning

CV = (SD / Mean) x 100 %

Coefficient of Variation FORMULA

Measure of Skewness

• Describes the degree of departures of the distribution of the data from symmetry.

• The degree of skevuness is measured by the coefficient of skevvness, denoted as SK and computed as, SK = 3 (Mean - Median) / SD

Symmetry

A distribution is said to be symmetric about the mean, if the distribution to the left of mean is the "mirror image" of the distribution to the right of the mean. Likewise, a symmetric distribution has SK=0 since its mean is equal to its median and its mode.

Measure of Kurtosis

Describes the extent of peakedness or flatness of the distribution of the data.

Box-and-Whiskers Plot

• Concerned with the symmetry of the distribution and incorporates measures of location in order to study the variability of the observations.

• Also called as box plot or 5-number summary (represented by Min, Max, QI, (22 , and Q3).

• Suitable for identifying outliers.

Box-and-Whiskers Plot

The diagram is made up of a box which lies between the first and third quartiles.

The whiskers are the straight lines extending from the ends of the box to the smallest and largest values that are not outliers.

STATISTICS

IT IS A SCIENTIFIC DISCIPLINE WHICH DEALS WITH THEORIES AND METHODS TO PROCESSS NUMERICAL INFORMATION.

DETERMINING THE EFFECTS OF ECQ TO THE PHILIPPINE ECONOMY

WHICH OF THE FOLLOWING IS NOT AN EXAMPLE OF DESCRIPTIVE STATISTICS?

A. NUMBER OF FILIPINOS WHO HAVE RECEIVED THE FIRST TRANCHE OF SAP

B. DETERMINING THE EFFECTS OF ECQ TO THE PHILIPPINE ECONOMY

C. CITING THE NUMBER OF ACASUALITIES IN TYPHOON AMBO

D. PRICE OF FUEL DURING ECQ

SAMPLE

IT IS A SUBSET OF THE POPULATION

PARAMETERS

THEY ARE CALLED NUMERICAL MEASURES THAT DESCRIBE THE POPULATION

TYPHOON NAMES

WHICH OF THE FOLLOWING IS A QUALITATIVE VARIABLE?
A. AGES OF SENIOR CITIZENS IN A BARANGAY

B. SALARIES OF SENIOR SUPERVISORS

C. AVERAGE TEMPERATURE OF A COVID 19 VICTIMS

D. TYPHOON NAMES

SPEED OF TYPHOON GORENG

WHICH OF THE FOLLOWING IS A DISCRETE VARIABLE?

A. P350 PER KILO OF TOMATO

B. SPEED OF TYPHOON GORENG

C. BODY TEMPERATURE OF A HUMAN BEING

D. NUMBER OF TYPHOONS IN A YEAR IN PH ISLANDS

PRICE INCREASE OF GASOLINE LAST TUESDAY

WHICH OF THE FOLLOWING IS A CONTINUOUS VARIABLE?

A. NUMBER OF CHILDREN IN A DAY CARE CENTER

B. HOSPITAL PATIENTS FROM TYPHOON GORENG

C. NUMBER OF ADU EMPLOYEES

D. PRICE INCREASE OF GASOLINE LAST TUESDAY

AN ECONOMICAL FORECASTS THE GNP NEXT YEAR TO BE 6.5%

WHICH OF THE FOLLOWING BELONG TO THE AREA OF INFERENTIAL STATISTICS?

A. AN ECONOMICAL FORECASTS THE GNP NEXT YEAR TO BE 6.5%

B. A STATISTICS TEACHER SHOWS A BAR GRAPH SHOWING THE NUMBER OF ENROLLEES PER COURSE

C. BOTH A AND B

D. NEITHER A AND B

QUALITATIVE

CELLULAR NUMBER AND ZIP CODE ARE EXAMPLES OF ___ VARIABLES

INTERVIEWS

WHICH OF THE FOLLOWING DOES NOT BELONG TO THE GROUP?

A. TV COMMERCIALS

B. FB POSTS

C. INTERVIEWS

D. VLOGS

FALSE

ANALYZING A GRAPHICAL PRESENTATION IS INFERENTIAL STATISTICS. TRUE OR FALSE?

A PATIENT NARRATES HIS EXPERIENCE OF COVID 19

WHICH OF THE FF IS CONSIDERED A PRIMARY DATA?

A. A PATIENT NARRATES HIS EXPERIENCE OF COVID 19

B. ONLINE CLASS

C. TV PATROL

D. YOUTUBE

DOWNPAYMENT FOR FIRST SEMESTER AY 2023-2024

WHICH OF THE FF IS A CONTINUOUS VARIABLE?

A. NUMBER OF UNITS ENROLLED IN A SEMESTER

B. DOWNPAYMENT FOR FIRST SEMESTER AY 2023-2024

C. NUMBER OF ONLINE TEACHERS

D. CLASS SCHEDULE OF BUSINESS STATISTICS

SUBJECT CODE

WHAT IS AN EXAMPLE OF A NOMINAL MEASUREMENT SCALE?

A. SUBJECT CODE

B. NUMBER OF SUBJECTS IN FIRST SEMESTER

C. TOTAL ONLINE CLASS HOURS

D. NUMBER OF ITEMS IN THIS ASSESSMENT

ORDINAL

WHICH MEASUREMENT SCALE DENOTES RANKING?

INTERVAL

TEMPERATURES ARE EXAMPLES OF __ MEASUREMENT SCALE.

DESCRIPTIVE STATISTICS

METHODS CONCERNED WITH COLLECTING, DESCRIBING, AND ANALYZING A SET OF DATA WITHOUT DRAWING CONCLUSIONS ABOUT A LARGE GROUP

RATIO

WEIGHTS OF THE ADU VOLLEYBALL TEAM ARE EXAMPLES OF __ MEASUREMENT SCALE