Business Statistics

2. Procedure & Objective
 Collected 30 samples [marks of statistics bridge course
and midterm exam], 10 samples each from PGDM A,
B, and C classes.
 Converted the marks to their percentages.
 Calculated the measures of Central Tendency and
measures of Dispersion.
 Analyse the relation between Bridge course marks and
midterm marks by using scatter diagram and Karl
Pearson’s Correlation coefficient.
 Hypothesis Testing on the midterm marks.

3. Data
Sl. No Bridge Midterm
1 70 28
2 50 17
3 40 20
4 43 37
5 77 73
6 57 67
7 83 33
8 80 70
9 73 40
10 60 50
11 60 80
12 83 90
13 47 73
14 70 55
15 63 88
Sl. No Bridge Midterm
16 67 23
17 37 53
18 70 58
19 50 73
20 37 48
21 80 27
22 63 20
23 80 27
24 83 43
25 80 47
26 47 47
27 80 73
28 90 93
29 73 80
30 70 53

4. Measures of Central Tendency
 Mean
The mean is the same of what is generally referred to as the
‘average’, and it is calculated in the following manner:
 Median
The median is the point corresponding to the score that lies in the
middle of the distribution (i.e., there are as many data points above
the median as there are below the median).
 Mode
The value that is repeated most often in the data set

5. Measures of Central Tendency
of Mid Term & Bridge Course
Marks
MEAN MEDIAN MODE
MID TERM 52.866% 51.5% 73%
BRIDGE 65. 433% 65% 80%

6. Measures of Dispersion
 Standard Deviation
The standard deviation measures the amount of variation or
dispersion from the average. It is represented by the Greek letter
sigma, σ.
 Variance
Variance measures how far a set of numbers is spread out. It is
denoted by for population and s2 for sample.

7. Measures of Dispersion of
Midterm & Bridge Course
Standard Deviation Variance
Midterm Exam 22.854 522.326
Bridge Course 15.525 250.27

8. SPSS Output

9. Correlation
 Scatter Diagram
A scatter diagram is a graph that shows the relationship between two
quantitative variables measured on the same individual. Each individual in
the data set is represented by a point in the scatter diagram.
 Karl Pearson's Correlation Coefficient
It summarizes the strength of linear relationship between two metric
variables i.e. ratio or interval variables.
 It ranges from +1 to -1.
 Correlation of +1: there is perfect positive relation between
variables.
 Correlation of -1 : there is perfect negative relation between
variables.
 Correlation is 0 : there is no relationship between variables.

10. Scatter Diagram

11. Regression and Co-relation
Coefficient

12. Interpretation
 From the scatter diagram it is clear that the
relation is positive and it is not a strong
relation.
 From the SPSS output it is clear that
correlation coefficient; r = 0.203, which implies
that the relation between Bridge marks and
midterm marks are weak & positive.
 The value of Coefficient of determination;
r² = .0412 means that only 4.12% of the total
variation of the midterm marks can be
explained by linear relationship between
bridge marks.

13. Hypothesis Testing – ‘T test’
 Why T test?
1. Population standard deviation of the
data is not known.
2. Sample size is 30.

14. T test for Midterm
 H˳ ≥ 40
H1 < 40
 One tailed test
Left tailed test
 Assume level of significance, α = 5%
 From SPSS; Zcal = 3.084
 From T table; Zcr = 1.699
 From SPSS; P value = 0.004
0.5 0.5
0.05

15. SPSS Output

16. T test for Bridge Course
 H˳ ≥ 40
H1 < 40
 One tailed test
Left tailed test
 Assume level of significance, α = 5%
 From SPSS; Zcal = 8.802
 From T table; Zcr = 1.699

18. Rejection Rules
 Rejection rule using p-value:
Reject H0 if p-value ≤ α
 Rejection rule using critical value:
Reject H0 if |TSCAL| > |TSCR|

19. Test Result
Result for Mid Term Exam
 Critical value approach:
|Zcal| > |Zcr| (3.084>1.699)
Hence the Null Hypothesis H˳ is
rejected.
Result for Bridge Course
 Critical value approach: 8.802 >1.699
Hence the Null Hypothesis H˳ is rejected.

20. Test Result
 P value approach:
P value < α (.004 < .05)
Hence the Null Hypothesis H˳ is rejected.

21. Conclusion
 Using SPSS data was analysed and we
calculated
1. Measures of central tendency and
measures of dispersion.
2. By studying co-relation we found that the
relation between bridge course marks and
midterm marks are weak and positive.
3. Hypothesis testing is done using P value
approach and critical value
approach and found out that null
hypothesis is rejected.
4. Hence it is clear that the percentage marks
of most of the students lies below 40%.