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