business statistics
DESCRIPTION
TRANSCRIPT
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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