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1. Descriptive statistics
and
Regression
Business Statistics ii

2. Welcome to our
Presentation

3. Content
• Part – 01
1. Frequency distribution table
2. Arithmetic mean, Median, Mode
3. Mean Deviation
4. Population Variance and Population Standard Deviation.
5. Geometric Mean
6. Sample Variance and Sample Standard Deviation.
7. Coefficient of Variation.
• Part – 02
1. Excel output
2. Multicolinearity

4. Part – 01
Descriptive statistics

5. Height of 20 students of Statistics(ii)
class :

6. Questions :
• Constract a frequency distribution table using both inclusive
and exclusive method.
• What is the value of data range?
• Find out Arithmatic mean.
• What is the value of Median?
• Find out mode.
• Determine the Mean Deviation.
• Find out Population Variance and Population Standard
Deviation.
• Determine the Geometric Mean from the above data.
• Find out Sample Variance and Sample Standard Deviation.
• What will be the Coefficient of Variation?

7. •Constract a frequency distribution table:
2k>n
25 (32) >20
So, Number of classes, K=5
i ≥
=
k
LH 
02.0
5
0.511.5



8. INCLUSIVE METHOD (If Interval=3):
Classes Frequency Relative
Frequency
Cumulative
Frequency
5.0 -5.2 3 0.15 3
5.3 – 5.5 5 0.25 8
5.6 – 5.8 11 0.55 19
5.9 – 5.11 1 0.05 20
5.12 – 6.1 0 0 20
Total 20

9. EXCLUSIVE METHOD (If Interval=3):
Classes Frequency Relative
Frequency
Cumulative
Frequency
5.0 to 5.3 3 0.15 3
5.3 to 5.6 5 0.25 8
5.6 to 5.9 11 0.55 19
5.9 to 5.12 1 0.05 20
5.12 to 6.2 0 0 20
Total 20

10. •Data Range:
Data Range= Highest – Lowest = 5.11-5.0= 0.11
• Arithmetic Mean:
µ =
= 5.5

11. •Arranging data from smallest to
Largest:
5.0, 5.0, 5.2, 5.3, 5.5, 5.5, 5.5, 5.5, 5.6, 5.6, 5.6,
5.6, 5.6, 5.7, 5.8, 5.8, 5.8, 5.8, 5.8, 5.11
Median =
𝐻−𝐿
𝐾
=
5.6+5.6
2
= 5.6
Mode
Modes are 5.6 and 5.8 (Highest occurrence of 5
times).

12. •Mean Deviation:
Mean Deviation =
𝑋−𝜇
𝑁
=
4.1
20
= 0.2

13. •Population Variance and STD:

14. •Geometric mean :
Geometric mean, GM =
Population Variance, 𝜎2 =
𝑋−𝜇 2
𝑁
=
1.33
20
= 0.0665
Population Standard Deviation,
𝜎 =
𝑋−𝜇 2
𝑁
=
1.33
20
= 0.258
= 5.5

15. • Sample Variance and STD:
𝑋 =
= 5.5

16. • Coefficient of Variation:
CV =
𝑆
𝑋
× 100
=
0.264
5.5
× 100
= 4.8%

17. Sample Variance, 𝑠2 =
(X − 𝑋)2
𝑛−1
=
1.33
20−1
= 0.07
Sample STD, s =
(X − 𝑋)2
𝑛−1
=
1.33
20−1
= 0.264

18. Part – 2
Regression

19. It is believed that Income per day of a CNG
driver is affected by gas expense per day and
number of trips per day. Results of the multiple
regression equation of Income per day on gas
expense per day and number of trips per day are
given below.

21. • Excel Output:

22. • Questions
1) Develop the Hypothesis
2) Find the equation of regression and Interpret.
3) Estimate the relationship among the variables in
relative terms.
4) Assess the explanatory power of the independent
variables.
5) Assess the significance of the results.
6) Ascertain whether there is a problem of
Multicollinearity.

23. Correlation Matrix: