Question 1
a. The histograms of the data are as follows:
b. Calculating for the 1.5xIQR rule:
For the Donating Scores, there are 5 exceptionally high outliers. For the Helping Score, there appears to be no outliers. For the Volunteering Score, there is 1 exceptionally high outlier.
c. Donating Money
The shape of the distribution is skewed to the left. There are 3 outliers that are all exceptionally high in value. The values of these outlier scores are 77, 78 and 91. The left skew is verified by the boxplot in which a large portion of the data is located on lower values, and the central value is also on the lower half.
Helping a Stranger
The shape of the distribution is near-perfect bell shape. There are no outliers, and the boxplot shows the same. The boxplot shows an almost symmetrical figure.
Volunteering Time
The shape of the distribution is skewed to the left. There are no outliers found, and is verified by the boxplot. The boxplot shows that the central value is slightly lower, and a majority of the data is located on the lower values.
It is observed that the most applicable measure of central tendency is the mean, and the most applicable measure of dispersion is the standard deviation. The data involved are numerical and quantitative, thus mean and standard deviation are the most practical measures of comparison.
d. Based on the sums and the means of the data, the countries seem to exert the most time in “Helping a Stranger”, and exert the least time in “Volunteering”. The three exceptionally high countries on “Donating Money” is a good indication of how these countries value the act of donating. This is because in this distribution, a huge number of the countries have very low donating scores. On the three scores, Australia scored above the mean or above average. Actually, the scores of Australia are all above Quartile 3. Therefore, based on the data, Australia is on the upper 25% of countries in World Giving.
Question 2
a. The 100% stacked column chart is:
b. Participate in a Fundraiser
P=No. of Fundraiser ParticipantsTotal Population=2761570=0.175796
c. i. Generation Y: P=Gen.Y FundraisersTotal Fundraisers=70276=0.253623
ii. Generation X: P=Gen.X FundraisersTotal Fundraisers=76276=0.275362
iii. Baby Boomers: P=Baby Boomer FundraisersTotal Fundraisers=85276=0.307971
iv. Matures: P=Mature FundraisersTotal Fundraisers=45276=0.163043
d. Mobile:
P=No. of Mobile ParticipantsTotal Population=1441570=0.09172
c. i. Generation Y: P=Gen.Y MobileTotal Mobile=54144=0.375
ii. Generation X: P=Gen.X MobileTotal Mobile=42144=0.291667
iii. Baby Boomers: P=Baby Boomer MobileTotal Mobile=43144=0.298611
iv. Matures: P=Mature MobileTotal Mobile=5144=0.034722
e. It is observed that “Mail” is the more used by the older generations, and the usage declines towards the younger generations. In contrast, “Mobile” is the preferred method of the younger generations, and this usage is declining towards older generations. This signifies the technology gap between the old and young. Also an observable trend is the “Fundraiser” method, in which more young generations prefer it compared to older generations.
Question 3
a. The decision variables are:
Objective is to reach the largest possible audience:
Objective Function: 5000R+2400F+2800N=Maximum
Constraints:
800R+240F+320N≤8000; 240F+320N≤2400
R≤12, F≤25, N≤20
F+N≥5
b. The output of the solver from Excel is:
c. The optimized number of radio spots is 7; this is less than the maximum allowed constraint of 12. The optimized number of flyers is 10; this is less than the maximum allowed constraint of 25. The number of newspaper ads is 0, which is less than the maximum 25. Since the advertisement options did not reach their maximum constraints, the shadow prices cannot be determined directly from them. It should be noted that the non-zero minimum constraint of the number of print-based ads (5) is reached (total print-based ads is 10).
d. If the budget is increased to $12000, the optimized number of radio spots is 12, which is equal to the maximum constraint. The number of flyers (10) and the number of newspaper ads (0) are still the same as the previous budget. The new number of reached audience is 84000. The results of the solver are shown in the following:
e. The optimal solution becomes 2 radio spots, 24 flyers, and 2 newspaper ads, and the total audience reached is 73200. This solution is different from the first run. The audience reached is much greater than the initial setting.
f. Recommendations: Increasing the budget definitely increases the number of audience reached. If choosing between print ads and radio while maintaining a budget, it is practical to allocate more funds and allowing lesser constraints for the print ads in order to reach a broader audience.
Question 4
a. The scatterplot is shown in the following:
There seems to be a trend occurring in the data; the trend is increasing on-line orders as unique visits increase. Therefore, it is appropriate to add a regression line to model this trend.
b. The scatterplot with the trend line is shown in the following:
The intercept (0.795) is close to zero, which is expected because there should be no online order/s if nobody is visiting in the first place. The slope (0.0752) shows that there is a slightly increasing trend of on-line orders as number of unique visits increases. The coefficient of determination (0.8388) shows that the trendline closely models the data because its value is close to 1.
c. Using the regression line formula: y=0.0752x+0.795
If the number of unique visits x=80000, then the number of expected on-line orders is:
y=0.075280000+0.795=6016.795≈6016
The conversion rate is: 601680000=0.0752→752 on-line orders per 10000 unique visits
Since the coefficient of determination is close to 1, and the derived conversion rate is equivalent to the slope of the regression line, the predictions are fairly accurate statistically.
d. It is observed that as the number of unique visits increases, the number of on-line orders also increases. Conversely, if the number of unique visits decreases, the number of on-line orders also decreases. Therefore, by ensuring that the number of unique visits is high, the number of on-line orders will reach the desired high mark.
