Business statistics
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The document contains a frequency distribution table that summarizes data from a questionnaire regarding a university computer service system. The table includes frequencies and percentages for respondent demographics like gender (72% male, 28% female), age group (50% between 21-23 years old, 34% 24-26, 16% over 26), GPA range, and academic program of study. A second section of the questionnaire assessed satisfaction levels of system quality on a 5-point scale.
Business statistics
- 2. 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
- 3. 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
- 4. 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.
- 5. Business Statistics: Statistics is the study of how to collect, organize, analyze, and interpret numerical information from data. Descriptive statistics involves methods of organizing, picturing and summarizing information from data. Inferential statistics involves methods of using information from a sample to draw conclusions about the Population. Individuals and Variables Individuals are the people or objects included in the study. A variable is the characteristic of the individual to be measured or observed. 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)
- 6. 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.
- 7. 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.
- 8. 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.
- 9. I. Qualitative data II. 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.
- 10. Further qualitative data has two types I. Discrete qualitative data II. 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
- 11. 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).
- 13. Frequency Distribution Relative Frequency distribution Percent frequency BAR GRAPH pie chart
- 14. Frequency Distribution A frequency distribution is tabular summary of showing the number(frequency) of items in each of several non over lapping classes. Relative Frequency A Relative Frequency distribution give a tabular summary of data showing the relative frequency for each class. Percent frequency Percent frequency summarize the percent frequency of data for each class. BAR GRAPH A bar graph is a graphical device for depicting qualitative data.
- 15. Pie Chart:- The pie chart is a commonly used graphical device for presenting relative frequency distributions for qualitative data.
- 16. Frequency Distribution Relative Frequency Percent Frequency Distributions Cumulative Distributions Dot Plot Histogram Ogive/ Frequency Polygon
- 17. 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
- 18. Relative Frequency A Relative Frequency distribution give a tabular summary of data showing the relative frequency for each class.
- 19. Percent frequency Percent 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
- 20. 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
- 21. 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.
- 22. 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.
- 23. 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.
- 24. Descriptive Statistics: Numerical Methods: Measures of Location Mean Median Mode Percentile Quartile Mean:- Mean are average value of all observation. The mean provides a measure of central location for the data. n xi Sample Mean= i 1 x1 x2 xn x n n
- 25. Sample Mean:- xi x n Where the numerator is the sum of values of n observations, or: Median:- xi x1 x2 ... xn 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
- 26. 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 p Step 3. 100 n 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.
- 27. 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 percentile Q2= 50th Percentile (also the Median) Q3= 75th percentile Measures of Variability Range Interquartile Range Variance Standard Deviation Coefficient of Variation
- 28. Range: Range is the difference largest value and smallest value Range = Largest Value – Smallest Value Interquartile Range: The difference between third quartile Q3 and first quartile Q1 IQR= Q3 – Q1 Variance: Variance is based on difference between value of each observation and the mean. Population Variance: 2 ( xi x ) 2 Sample Variance= s n 1
- 29. 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. 2 s s If the data set is a population, the standard deviation is denoted (sigma). 2
- 30. Coefficient of Variation: In descriptive statistics that indicates how large a standard deviation is relative to the mean. s CV 100% Sample= x σ Population= CV 100% μ
- 31. 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. xi x zi s 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.
- 32. 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
- 33. 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. ( xi x )( yi y ) s xy n 1 If the data sets are populations, the covariance is denoted by ( xi x )( yi y ) xy N
- 34. 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. s xy rxy sx s y If the data sets are populations, the coefficient is xy xy x y
- 36. Frequency Distribution W R T Gender CLASSES Cumulative Frequency Percent Percent Male 36 72.0 72.0 Female 14 28.0 100.0 Total 50 100.0
- 37. Classes Cumulative Frequency Percent Percent 21-23 25 50.0 50.0 24-26 17 34.0 84.0 >26 8 16.0 100.0 Total 50 100.0
- 38. Classes Cumulative Frequency Percent Percent 1-1.5 4 8.0 8.0 1.5-2 6 12.0 20.0 2-2.5 12 24.0 44.0 2.5-3 11 22.0 66.0 3-3.5 1 2.0 68.0 3.5-4 16 32.0 100.0 Total 50 100.0
- 39. BBA 15 30.0 30.0 30.0 MBA 14 28.0 28.0 58.0 MS 5 10.0 10.0 68.0 MDM 4 8.0 8.0 76.0 OTHERS 12 24.0 24.0 100.0 Total 50 100.0 100.0
- 40. Classes Cumulative Frequency Percent Percent Completely 20 40.0 40.0 Dissatisfied Disagree 8 16.0 56.0 Neutral 11 22.0 78.0 Satisfied 9 18.0 96.0 completely 2 4.0 100.0 satisfied Total 50 100.0
- 41. Classes Cumulative Frequency Percent Percent Completely 7 14.0 14.0 Dissatisfied Disagree 16 32.0 46.0 Neutral 10 20.0 66.0 satisfied 12 24.0 90.0 completely 5 10.0 100.0 satisfied Total 50 100.0
- 42. Classes Cumulative Frequency Percent Percent Completely 9 18.0 18.0 Dissatisfied Disagree 8 16.0 34.0 Neutral 21 42.0 76.0 Satisfied 9 18.0 94.0 completely 3 6.0 100.0 satisfied Total 50 100.0
- 43. Classes Cumulative Frequency Percent Percent Completely 5 10.0 10.0 Dissatisfied Disagree 11 22.0 32.0 Neutral 14 28.0 60.0 satisfied 12 24.0 84.0 completely 8 16.0 100.0 satisfied Total 50 100.0
- 44. Classes Cumulative Frequency Percent Percent Completely 7 14.0 14.0 Dissatisfied Disagree 11 22.0 36.0 Neutral 14 28.0 64.0 Satisfied 9 18.0 82.0 completely 9 18.0 100.0 satisfied Total 50 100.0
- 45. GENDER Std. Minim Maxim Deviati Varian Classes N Range um um Mean on ce Freque ncy Distribu 50 1.00 1.00 2.00 1.2800 .45356 .206 tion W RT Gender Valid N (listwis 50 e)
- 46. Classes Std. Minimu Maximu Deviatio Varianc N Range m m Mean n e Frequen cy Distributi 50 2.00 3.00 5.00 3.6600 .74533 .556 on W R T Age Valid N 50 (listwise)
- 47. Classes Std. Minimu Maximu Deviatio Varianc N Range m m Mean n e Frequen cy Distributi 50 5.00 2.00 7.00 4.9400 1.67100 2.792 on W R T CGPA Valid N 50 (listwise)
- 48. Classes Std. Minimu Maximu Deviatio Varianc N Range m m Mean n e Frequen cy Distributi 50 4.00 1.00 5.00 2.6800 1.57065 2.467 on W R T Class Valid N 50 (listwise)
- 49. Classes Std. Minimu Maximu Deviatio Varianc N Range m m Mean n e The usefulne ss of 50 4.00 1.00 5.00 2.3000 1.28174 1.643 system function s. Valid N 50 (listwise)
- 50. Classes Std. Minimu Maximu Deviatio Varianc N Range m m Mean n e The up- to-date of 50 4.00 1.00 5.00 2.7800 1.13011 1.277 platform s. Valid N 50 (listwise)
- 51. Classes Std. Minimu Maximu Deviatio Varianc N Range m m Mean n e The necessit y of 50 4.00 1.00 5.00 3.1400 1.22907 1.511 system function s. Valid N 50 (listwise)
- 52. Clas Std. Minimu Maximu Deviatio Varianc ses N Range m m Mean n e The stability of 50 4.00 1.00 5.00 3.0400 1.30868 1.713 systems . Valid N 50 (listwise)
- 53. The Usefulness of System Functions Completely Dissatisfied Disagree Neutral Satisfied Completely Satisfied