assignment
Subject Code: ECOM90009
Subject Name: Quantitative Methods for Business
Assignment Number: 2
Workshop Day and Time: Thursday 02:15pm
Tutor Name: Jackson Yuen
Student ID Number
Student Name
1.
2.
3.
4.
Question 1:
a.
Count
150
Mode
22
Sum
3231
Standard Deviation
4.728
Range
29
Sample Variance
22.357
Maximum
36
Coefficient of Variance
0.22
Minimum
7
Mad
3.0
Mean
21.54
25th percentile
18.5
Median
22
75th percentile
25
The central location of the distribution includes mean, median and mode. As illustrated above, the mean number, median number and mode number of the distribution of installation times are 21.54,22 and 22. There are little differences among the three numbers which means that the shape of the distribution is nearly symmetric.
The variance of the installation time of this sample is 22.357 while the standard deviation is 4.728. The installation time ranges from 7 minutes to 36 minutes. The coefficient of variance is 0.22 which is low. The mad of the sample is 3.0.
The first quartile is 18.5 indicating that 25% of the purchasers’ installation time is less than 18.5 minutes. However the third quartile is 25 which shows that 75% of the purchasers spent less than 25 minutes to install the software.
b.
Yes, we are able to estimate the mean installation time using this data. We do not know the variance of the population so we need to standardise the mean of the installation time and use the sample standard deviation as an estimate of , creating a Student t distribution.
Before using the t statistic estimator with the absence of , we should guarantee that the underlying data must be normally distributed or at least not extremely non-normal. In order to check this condition, we are able to draw a histogram using our data. Besides, we also assume that the population is normally distribution.
We can see that the histogram is a reasonable bell-shape.
A single
Subject Name: Quantitative Methods for Business
Assignment Number: 2
Workshop Day and Time: Thursday 02:15pm
Tutor Name: Jackson Yuen
Student ID Number
Student Name
1.
2.
3.
4.
Question 1:
a.
Count
150
Mode
22
Sum
3231
Standard Deviation
4.728
Range
29
Sample Variance
22.357
Maximum
36
Coefficient of Variance
0.22
Minimum
7
Mad
3.0
Mean
21.54
25th percentile
18.5
Median
22
75th percentile
25
The central location of the distribution includes mean, median and mode. As illustrated above, the mean number, median number and mode number of the distribution of installation times are 21.54,22 and 22. There are little differences among the three numbers which means that the shape of the distribution is nearly symmetric.
The variance of the installation time of this sample is 22.357 while the standard deviation is 4.728. The installation time ranges from 7 minutes to 36 minutes. The coefficient of variance is 0.22 which is low. The mad of the sample is 3.0.
The first quartile is 18.5 indicating that 25% of the purchasers’ installation time is less than 18.5 minutes. However the third quartile is 25 which shows that 75% of the purchasers spent less than 25 minutes to install the software.
b.
Yes, we are able to estimate the mean installation time using this data. We do not know the variance of the population so we need to standardise the mean of the installation time and use the sample standard deviation as an estimate of , creating a Student t distribution.
Before using the t statistic estimator with the absence of , we should guarantee that the underlying data must be normally distributed or at least not extremely non-normal. In order to check this condition, we are able to draw a histogram using our data. Besides, we also assume that the population is normally distribution.
We can see that the histogram is a reasonable bell-shape.
A single