Session 1_Introduction Managerial Statistics

8/3/2019 Session 1_Introduction Managerial Statistics

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Quantitative Method ±I

Managerial Statistics

Introduction



Statistics is a mathematical science pertaining to

± Collection

± Analysis

± Interpretation

± Explanation ± Presentation of data

Data is an information

± When it is organized ± Otherwise it is a measurement.



Application of Statistics is found in a wide variety of

academic disciplines ± Physical sciences

± Social sciences

± Medical Sciences

± Humanities. ± It is also used for making decisions in all areas of business

and government.

Application of statistical technique is so diverse that it is

commonly separate into two broad categories:1. Descriptive Statistics

2. Inferential Statistics



Descriptive statistics are used to describe the basic features of the data in a study. They provide simple summaries about the

sample and the measures.

Techniques used to summaries the data are:

Graphs

Tables

Calculate certain values (i.e. percentage)

Steps in descriptive statistics:

1. Collect data

2. Classify data 3.Summarize data

4.Present data

5. Proceed to inferential statistics if there are enough data todraw a conclusion



Inferential statistics are drawn inferences about a populationfrom a sample.

A population consists of an entire observations, that have

something in common

A sample is a subset of a population.

There are two main methods used in inferential statistics:

Estimation

Hypothesis testing. Some other methods are used in inferential statistics:

prediction, probability, etc.



R aw Data

Table 1

Carpet (in yards) produced by each of the 30 looms in one days sample

16.2 15.4 16.0 16.6 15.9 15.8 16 16.8 16.9 16.8

15.7 16.4 15.2 15.8 15.9 16.1 15.6 15.9 15.6 16.0

16.4 15.8 15.7 16.2 15.6 15.9 16.3 16.3 16.0 16.3

Information before the data arranged is called raw data. It is raw

because it is unprocessed by statistical methods

Dalmon carpet company has for 500 carpet looms



Data ArrayAn arrangement of raw data in ascending and descending order of

magnitude is called an array.

Table 2

Raw data of daily production in yards

of 30 carpet looms

16.9 16.4 16.2 16.0 15.8 15.6

16.8 16.3 16.1 15.9 15.8 15.6

16.8 16.3 16.0 15.9 15.8 15.6

16.6 16.3 16.0 15.9 15.7 15.4

16.4 16.2 16.0 15.9 15.7 15.2

Table 3

Data array of daily production in

yards of 30 carpet looms

15.2 15.7 15.9 16.0 16.2 16.4

15.4 15.7 15.9 16.0 16.3 16.6

15.6 15.8 15.9 16.0 16.3 16.8

15.6 15.8 15.9 16.1 16.3 16.8

15.6 15.8 16.0 16.2 16.4 16.9





Frequency Distribution (Ungroup Data)

Table 2

Frequency distribution of average inventory (in days) for 20 convenience store

Avg. Inventory Frequency Avg. Inventory Frequency

2 1 4.3 1

3.4 2 4.7 2

3.8 2 4.8 1

4 1 4.9 2

4.1 3 5.5 4

4.2 1



Frequency Distribution (Group Data)

Table 1

Data Array of Average Inventory (in days) for 20 Convenience Store

2 3.8 4.1 4.7 5.5

3.4 4 4.2 4.8 5.5

3.4 4.1 4.3 4.9 5.5

3.8 4.1 4.7 4.9 5.5

Condense the data into classes or groups of value describing

some characteristics of the data is called frequency distribution

of group data



Frequency Distribution (Group Data)

Table 3

Frequency distribution of average inventory (in days) for 20 convenience

stores (6 classes)

Class (group of Similar Values of

Data Points)

Frequency (Number of Observation in

Each Class)

2.0 to 2.5 1

2.6 to3.1 0

3.2 to 3.7 2

3.8 to 4.3 8

4.4 to 4.9 5

5.0 to 5.5 4



R elative frequency distribution

Table 6

Relative frequency distribution of average inventory (in Days) for 20 StoresClass Frequency Relative Frequency:

2.0 to 2.5 1 0.05

2.6 to 3.1 0 0.00

3.2 to 3.7 2 0.103.8 to 4.3 8 0.40

4.4 to 4.9 5 0.25

5.0 to 5.5 4 0.20

Total 20 1.00

Frequency of each observation as a fraction or percentage of thetotal number of observation is called relative frequency

distribution



Class Interval

Table 1Yards produced by each of the 30 looms in yesterdays sample

16.2 15.4 16 16.6 15.9 15.8 16 16.8 16.9 16.8

15.7 16.4 15.2 15.8 15.9 16.1 15.6 15.9 15.6 16

16.4 15.8 15.7 16.2 15.6 15.9 16.3 16.3 16 16.3

Width of class interval = [next unit value after largest value in

data ±smallest value in the data]/total number of class



Class Interval

Table 7

Daily production in a sample of 30 Carpet looms with 0.3 yard class interval

class Width of class intervals Frequency

15.2-15.4 0.3 2

15.5-15.7 0.3 5

15.8-16.0 0.3 11

16.1-16.3 0.3 6

16.4-16.6 0.3 3

16.7-16.9 0.3 3



Histogram

Table 7


class Frequency

15.2-15.4 2

15.5-15.7 515.8-16.0 11

16.1-16.3 6

16.4-16.6 3

16.7-16.9 3

Histogram is a graphical representation of a frequency distributionin the form of rectangles one after other with height proportional

to the frequency



Figure1: Histogram



R elative FrequencyHistogram

Table 8

Relative Frequency Daily production in a sample of 30 Carpet looms with 0.3

yard class interval

class Frequency Relative Frequency15.2-15.4 2 0.07

15.5-15.7 5 0.17

15.8-16.0 11 0.37

16.1-16.3 6 0.2016.4-16.6 3 0.10

16.7-16.9 3 0.10



Figure 2: R elative Frequency Histogram



Figure 3: Frequency Polygon

Table 7


class Frequency

15.2-15.4 2

15.5-15.7 5

15.8-16.0 1116.1-16.3 6

16.4-16.6 3

16.7-16.9 3

A frequency polygon is simply a line graph that connects the mid

points of all the bar of the histogram



Figure 3: Frequency Polygon



Cumulative Frequency Distribution

Table 8

Frequency daily production in a sample of 30 Carpet looms with 0.3 yard classinterval

class Frequency

15.2-15.4 2

15.5-15.7 5

15.8-16.0 11

16.1-16.3 6

16.4-16.6 3

16.7-16.9 3

A cumulative frequency distribution gives us to see the number of observations lie above and bellow certain value



Cumulative Frequency Distribution

Table 9

Cumulative less than frequency distribution of production levels in a sample of

30 Carpet looms

Class Cumulative Frequency

Less Than 15.2 0

Less Than 15.5 2

Less Than 15.8 7

Less Than 16.1 18Less Than 16.4 24

Less Than 16.7 27

Less Than 17.0 30



Figure 4:Less Than OgiveA graph of cumulative frequency distribution is called Ogive

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Session 1_Introduction Managerial Statistics