Business statistics

Bus

ines

s

Stat

istics

Bilal Khan Niazi 11-Arid-1314 Naveed Ahmed 11-Arid-1322 Asad Mehmood 11-Arid-1294 Arslan Akbar 11-Arid-1293 Salik Atta 11-Arid-1326 Zeeshan Gohar 11-Arid-1335 Ijaz-ull-Hassan 11-Arid-1185

GROUP NO: 4

Group-4 QUESTIONNAIRE System Quality of University Computer Service

System Section I Respondent profile 1. Gender? Male Female 2. Age? 15-17 18-20 21-23 24-26 More than 35 3. CGPA: 0.5-1 1-1.5 1.5-2 2-2.5 2.5-3 3-3.5 3.5-4

4. What is your class?BBA MBA MS MDM Other

Section II (Completely Dissatisfied = 1, Dissatisfied = 2,

Neutral = 3, Satisfied = 4, completely satisfied = 5)

System Quality 1 2 3 4 5

1. The usefulness of system functions.

2. The friendliness of users interfaces.

3. The up-to-date of platforms.

4. The necessity of system functions.

5. The stability of systems.

6. The response time of system.

7. The duration of system update.

Business Statistics: Statistics is the study of how to collect, organize, analyze, andinterpret numerical information from data. Descriptive statisticsinvolves methods of organizing, picturing and summarizinginformation from data. Inferential statistics involves methods ofusing information from a sample to draw conclusions about thePopulation. Individuals and VariablesIndividuals are the people or objects included in the study. Avariable is the characteristic of the individual to be measured orobserved.There is no assumption in the descriptive statistics. It is related

to the facts and figure.Descriptive statistics measure the central tendency(Mean median, mode, percentile, and quartile)Measure of desperation (Range, inter-quarter range, variance,

standard deviation, coefficient of variable)

Inferential statistics: Inferential Statistics: A decision, estimate, prediction, or

generalization about a population, based on a sample. Inferential deal with the assumption and future forecasting.

Data and data set:Data is a raw facts and figure. That are collected,

summarized, analyzed, and interpreted.The data collected in a particular study are referred to as the

data set.

Scales of measurement: Scales of measurement include:

◦ Nominal◦ Ordinal◦ Interval◦ Ratio

The scale determines the amount of information contained in the data.

The scale indicates the data summarization and statistical analyses that are most appropriate.

Types of data:

Nominal Scale: Data that is classified into categories and cannot be

arranged in any particular order. For example male-female, Pakistani etc.

Ordinal scale: It categorizes and ranks the variables according to the

preferences. For example from best to worst, first to last, a numeric code may be used.

Interval scale: To put the interval in the order data. It fulfills the

characteristics of nominal and ordinal scale. Ratio scale: The data have all the properties of interval data and the

ratio of two values is meaningful. Variables such as distance, height, weight, and time use the ratio scale. This scale must contain a zero value.

I. Qualitative dataII. Quantitative data Qualitative data:Qualitative is related to the non-numeric form of data. For

example, male and female, members of the family, eye color.

Quantitative data:Quantitative data is related to the numeric form of data. For

example, age, CGPA, income.Quantitative data indicate either how many or how much.Quantitative data are always numeric.

Types of variables:

Further qualitative data has two typesI. Discrete qualitative dataII. Continues qualitative data  Discrete qualitative data: Quantitative data that measure how

many are discrete.(how many students in the class) Continues data:Quantitative data that measure how much are continuous. (GPA,

income) Cross-Sectional and Time Series Data: Cross-sectional data: Are collected at the same or approximately the same point in time.Example: data detailing the number of building permits issued in

June 2000 Time series data:Are collected over several time periods.Example: data detailing the number of building permits issued in

Travis County, Texas in each of the last 36 months

Descriptive Statistics: Descriptive statistics are the tabular, graphical, and

numerical methods used to summarize data. Statistical Inference: Statistical inference is the process of using data obtained

from a small group of elements (the sample) to make estimates and test hypotheses about the characteristics of a larger group of elements (the population).

Descriptive Statistics:

Tabular and Graphical

Methods:

Frequency Distribution Relative Frequency distribution Percent frequency BAR GRAPH pie chart

Summarizing the Qualitative Data

Frequency Distribution A frequency distribution is tabular summary of showing the

number(frequency) of items in each of several non over lapping classes.

Relative FrequencyA Relative Frequency distribution give a tabular summary of

data showing the relative frequency for each class. Percent frequencyPercent frequency summarize the percent frequency of data

for each class. BAR GRAPHA bar graph is a graphical device for depicting qualitative

data.

Pie Chart:-The pie chart is a commonly used graphical device for

presenting relative frequency distributions for qualitative data.

Frequency Distribution Relative Frequency Percent Frequency Distributions Cumulative Distributions Dot Plot Histogram Ogive/ Frequency Polygon

Summarizing Quantitative Data

Frequency Distribution A frequency distribution is tabular summary of showing the

number(frequency) of items in each of several non over lapping classes.

Classes Frequency

Male 36

Female 14

Total 50

Classes Frequency

21-23 25

24-26 17

>26 8

Total 50

Relative FrequencyA Relative Frequency distribution give a

tabular summary of data showing the relative frequency for each class.

Percent frequencyPercent frequency summarize the percent

frequency of data for each class.

Classes Percent Frequency

Male 72

Female 28

Total 100

Classes Percent Frequency

21-23 50.00

24-26 34.00

>26 16.00

Total 100.00

Cumulative frequency distribution -- shows the number of items with values less than or equal to the upper limit of each class.

Classes C.F.D

Male 72

Female 100

Classes C.F.D

21-23 50.0

24-26 84.0

>26 100.0

Cumulative relative frequency distribution -- shows the proportion of items with values less than or equal to the upper limit of each class.

Cumulative percent frequency distribution -- shows the percentage of items with values less than or equal to the upper limit of each class.

Dot Plot  One of the simplest graphical summaries of data is a dot

plot. A horizontal axis shows the range of data values. Then each data value is represented by a dot placed above

the axis. Histogram Another common graphical presentation of quantitative

data is a histogram. The variable of interest is placed on the horizontal axis. A rectangle is drawn above each class interval’s frequency,

relative frequency, or percent frequency. Unlike a bar graph, a histogram has no natural separation

between rectangles of classes.

  Ogive/ Frequency Polygon An ogive/ Polygon is a graph of a cumulative distribution.The data values are shown on the horizontal axis.Shown on the vertical axis are the:

◦ cumulative frequencies, or◦ cumulative relative frequencies, or◦ cumulative percent frequencies

The frequency (one of the above) of each class is plotted as a point.

The plotted points are connected by straight lines. Scatter Diagram:-Is a graphical presentation of the relationship between two

quantitative variables.

Descriptive Statistics: Numerical Methods: Measures of LocationMeanMedianMode PercentileQuartile   Mean:-Mean are average value of all observation. The mean

provides a measure of central location for the data.

Sample Mean=n

xxx

n

xx n

n

ii

211

Sample Mean:-

Where the numerator is the sum of values of n observations, or:

Median:- Median is the value in the middle when the data are

arranged in ascending order with an odd number of observations the mean is the middle value. An even number of observation has no single middle value in this case simply we average the middle two observations.

Mode:- The mode is the value that occurs with greatest frequency. Value that occurs most often There may be no mode There may be several modes

n

xx i

ni xxxx ...21

Percentiles:- The pth percentile is a value such that at least p percent of

the observations are less than or equal to this value at least (100-p) percent of the observations are greater than or equal to this value.

Calculating the Pth Percentile:- Step 1. Arrange the data in ascending order Step 2. Compute an index i Step 3. If i is not integer then round up. The next integer greater than

i denotes the position of the pth percentile .If i is an integer the pth percentile is the average of the

values in positions i and i+1.

np

100

Quartile:-It is often desirable to divide data in four parts, with each part

containing approximately one-fourth, or 25% of the observations.

Q1= 25th percentileQ2= 50th Percentile (also the Median)Q3= 75th percentile

Measures of Variability Range Interquartile Range Variance Standard Deviation Coefficient of Variation

Range:Range is the difference largest value and smallest valueRange = Largest Value – Smallest Value Interquartile Range:The difference between third quartile Q3 and first quartile Q1IQR= Q3 – Q1 Variance:Variance is based on difference between value of each

observation and the mean.Population Variance:

Sample Variance= 1

)( 22

n

xixs

Standard Deviation:Standard deviation is defined to be positive square root of the

variance. If the data set is a sample, the standard deviation is

denoted s.

If the data set is a population, the standard deviation is denoted (sigma).

2ss

2

Coefficient of Variation: In descriptive statistics that indicates how large a standard

deviation is relative to the mean.

Sample=

Population=

100%x

sCV

100%μ

σCV

Measure of Distribution Shapes:- Z-Score Outliers Z-Score: Z-score is often called the standardized value. The z-score

can be interpreted as the number of standard deviation is from the mean.

Outliers: Sometimes a data set will have one or more observation

with unusually large or unusually small values. These extreme values are called outliers. If the value is greater than ±3 then outlier exists.

s

xxz ii

Exploratory Data Analysis: Five Number Summary: Smallest Value First Quartile Median Third Quartile Largest Value Measure of Association between Two

Variables: Covariance Interpretation of Covariance Correlation Coefficient

Covariance:- The covariance is a measure of the linear association

between two variables. Positive values indicate a positive relationship. Negative values indicate a negative relationship. If the data sets are samples, the covariance is denoted by

sxy.

If the data sets are populations, the covariance is denoted by

1

))((

n

yyxxs iixy

N

yx yixixy

))((

Interpretation of Covariance: It tells us the relation between two variables is positive or

negative. Correlation Coefficient: The coefficient can take on values between -1 and +1. Values near -1 indicate a strong negative linear

relationship. Values near +1 indicate a strong positive linear

relationship. If the data sets are samples, the coefficient is rxy.

If the data sets are populations, the coefficient is

yx

xyxy ss

sr

yx

xyxy

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CLASSESFrequency Percent

Cumulative Percent

Male 36 72.0 72.0Female 14 28.0 100.0Total 50 100.0

Frequency Distribution W R T Gender

Classes Frequency PercentCumulative

Percent21-23 25 50.0 50.024-26 17 34.0 84.0>26 8 16.0 100.0Total 50 100.0

Frequency Distribution W R T Age

Classes Frequency PercentCumulative

Percent1-1.5 4 8.0 8.01.5-2 6 12.0 20.02-2.5 12 24.0 44.02.5-3 11 22.0 66.03-3.5 1 2.0 68.03.5-4 16 32.0 100.0Total 50 100.0

Frequency Distribution W R T CGPA

BBA 15 30.0 30.0 30.0MBA 14 28.0 28.0 58.0MS 5 10.0 10.0 68.0MDM 4 8.0 8.0 76.0OTHERS 12 24.0 24.0 100.0Total 50 100.0 100.0

Frequency Distribution W R T Class

Classes Frequency PercentCumulative

PercentCompletely Dissatisfied 20 40.0 40.0Disagree 8 16.0 56.0Neutral 11 22.0 78.0Satisfied 9 18.0 96.0completely satisfied 2 4.0 100.0Total 50 100.0

The usefulness of system functions.

Classes Frequency PercentCumulative

PercentCompletely Dissatisfied 7 14.0 14.0Disagree 16 32.0 46.0Neutral 10 20.0 66.0satisfied 12 24.0 90.0completely satisfied 5 10.0 100.0Total 50 100.0

The friendliness of users interfaces.

Classes Frequency PercentCumulative

PercentCompletely Dissatisfied 9 18.0 18.0Disagree 8 16.0 34.0Neutral 21 42.0 76.0Satisfied 9 18.0 94.0completely satisfied 3 6.0 100.0Total 50 100.0

The up-to-date of platforms.

Classes Frequency PercentCumulative

PercentCompletely Dissatisfied 5 10.0 10.0Disagree 11 22.0 32.0Neutral 14 28.0 60.0satisfied 12 24.0 84.0completely satisfied 8 16.0 100.0Total 50 100.0

The necessity of system functions.

Classes Frequency PercentCumulative

PercentCompletely Dissatisfied 7 14.0 14.0Disagree 11 22.0 36.0Neutral 14 28.0 64.0Satisfied 9 18.0 82.0completely satisfied 9 18.0 100.0Total 50 100.0

The stability of systems.

GENDER

RANGE ,MIN,MAX VALUES,MEAN, STANDERDEVIATION, VERIANCE

Classes N RangeMinim

umMaxim

um Mean

Std. Deviati

onVarian

ceFrequency Distribution W R T Gender

50 1.00 1.00 2.00 1.2800 .45356 .206

Valid N (listwise)

50

ClassesN Range

Minimum

Maximum Mean

Std. Deviatio

nVarianc

eFrequency Distribution W R T Age

50 2.00 3.00 5.00 3.6600 .74533 .556

Valid N (listwise)

50

AGE

ClassesN Range

Minimum

Maximum Mean

Std. Deviatio

nVarianc

eFrequency Distribution W R T CGPA

50 5.00 2.00 7.00 4.9400 1.67100 2.792

Valid N (listwise)

50

CGPA

ClassesN Range

Minimum

Maximum Mean

Std. Deviatio

nVarianc

eFrequency Distribution W R T Class

50 4.00 1.00 5.00 2.6800 1.57065 2.467

Valid N (listwise)

50

CLASS

ClassesN Range

Minimum

Maximum Mean

Std. Deviatio

nVarianc

eThe usefulness of system functions.

50 4.00 1.00 5.00 2.3000 1.28174 1.643

Valid N (listwise)

50

USEFULNESS OF SYSTEM

ClassesN Range

Minimum

Maximum Mean

Std. Deviatio

nVarianc

eThe up-to-date of platforms.

50 4.00 1.00 5.00 2.7800 1.13011 1.277

Valid N (listwise)

50

UPDATE OF SYSTEM

ClassesN Range

Minimum

Maximum Mean

Std. Deviatio

nVarianc

eThe necessity of system functions.

50 4.00 1.00 5.00 3.1400 1.22907 1.511

Valid N (listwise)

50

Necessity of system function

Classes N Range

Minimum

Maximum Mean

Std. Deviatio

nVarianc

eThe stability of systems.

50 4.00 1.00 5.00 3.0400 1.30868 1.713

Valid N (listwise)

50

Stability of system

Pie Chart

The Usefulness of System Functions

Completely DissatisfiedDisagreeNeutralSatisfiedCompletely Satisfied

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