L/508/0442 - Quantitative Methods Of Calculation Represent Mathematical Data

QUESTION 1

a. Stating the Frequency, Relative Frequency, Cumulative Relative Frequency and Class Midpoint

Measures of Variability and Association

Class interval	Number of passengers at each train station in Melbourne	Cumulative  frequency	Relative frequency	Cumulative relative frequency	mid point
169-468	19	19	0.32	0.32	403
469-768	12	31	0.20	0.52	853
769-1068	9	40	0.15	0.67	1303
1069-1368	8	48	0.13	0.80	1753
1369-1668	5	53	0.08	0.88	2203
1669-1968	2	55	0.03	0.92	2653
1969-2268	1	56	0.02	0.93	3103
2569-2868	2	58	0.03	0.97	4003
2869-3168	1	59	0.02	0.98	4453
7669-7968	1	60	0.02	1.00	11653
Grand Total	60	Â

 

Histogram

 

3. Descriptive statistics

Computation of mean, mode and median

Number of passengers at each train station in Melbourne
Particulars	Outcome
Mean	1033.43
Standard Error	141.11
Median	715
Mode	401
Standard Deviation	1093.04
Sample Variance	1194731
Kurtosis	23.78
Skewness	4.21
Range	7560
Minimum	169
Maximum	7729
Sum	62006
Count	60

 

The above depicted table of descriptive statistics show that average number of passengers at each train station in Melbourne accounts for 1033 respectively. Further, outcome of descriptive statistics present that 50% value of data set and median value implies for 715 significantly. Along with this, it has assessed from the evaluation that mode is 401. On the basis of this, it can be presented that 401 passengers repeatedly arrived at each train station in Melbourne for the weekday peak time such as 7 am to 9.29 am.      

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QUESTION 2

a. Assessing whether above given data comes under population or sample

            From research, it has found that data set given in relation to the weekly attendance in Holmes and number of chocolate bars sold. Referring given case, it can be presented that manager of supermarket wants to assess whether there is any relationship takes place between the students who attending class and sales of chocolate bars. Hence, in this, whole students of Holmes have been considered. Thus, by taking into such aspects it can be presented that given data set implies for population rather than sample. Moreover, sample is the small part of population, whereas population accounts for the whole target. Hence, it can be mentioned that given data set includes population. Through assessment, it has identified that significant difference takes place between sample and population (Cressie, 2015). Moreover, population implies for the collection of all elements who possess common characteristics that comprise universe.  

b. Calculating standard deviation of the weekly attendance

Computation of standard deviation

S. No.	Weekly attendance
1	472
2	413
3	503
4	612
5	399
6	538
7	455
Standard deviation	74.1

 

            Findings of statistical assessment presents that in the near future mean value will deviate from the figure of 74.1 respectively.

3. Inter-quartile range assessment

Interquartile range may be swerved as a viability measure which divides or distinguishes whole data set into quartiles. By subtracting 1^st quartile from the 3^rd one interquartile range can be assessed.

Calculation of inter-quartile range

Particulars	Number of chocolate bars sold
	6916
	5884
	7223
	8158
	6014
	7209
	6214
1st quartile	6114
3rd quartile	7216
Inter-quartile range (3rd quartile – 1st quartile)	1102

 

4. Assessing correlation co-efficient

Correlation is the most effectual statistical tool which helps in assessing the extent to which two variables are associated with each other. In other words, it helps in assessing the level to which one variable will move when changes take place in another. 

Correlation co-efficient

Weekly attendance	Number of chocolate bars sold
472	6916
413	5884
503	7223
612	8158
399	6014
538	7209
455	6214