1.4 What is the minimum age bin? Ans: 0 year

1.5 What is the maximum age bin? Ans: 55 years

1.6 What is the bin size for the age field? Ans: 1 year


2.1 Use the expected value for the age to find the mean age for the whole data sample. Ans: Expected Value is 27.800

## [1] 27.80027

2.2 Standard Deviation for whole data sample

Ans=Sample Standard Deviation= 15.778, the same as the population Standard Deviation of 15.778 to 3dp.

## [1] 15.77804
## [1] 15.77818

Question 3 Statistics of mean age for each region

3.1 Mean=30.608

3.2 SD=7.996

3.3 Minimum = 2

3.4 First Quartile = 27.426

3.5 Median = 29.232

3.6 Third Quartile = 33.35

3.7 Maximum = 55

3.8 IQR = 5.924

## [1] "1"
##     mean     sd min     Q1 Median    Q3 max    IQR
## 1 30.608 7.9962   2 27.426 29.232 33.35  55 5.9243

3.9 Histogram of the distribution of means

Question 4 Region with smallest population

SSC20099 is one of the regions with the smallest population of 3 people


## Rows: 35
## Columns: 2
## $ region <chr> "SSC20099", "SSC20127", "SSC20151", "SSC20346", "SSC20383", "SS~
## $ n      <dbl> 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, ~

Question 5 Region with largest population. Ans: Region is SSC22015 with population of 37948

From the plot in 5.1, it is observed that:

1. The population is highest around 3 and 30 years old.

2. The population declines from 4 to 20, and beyond 30 years old.

3. The trend suggests that the region is populated by mainly young families with young children.

## # A tibble: 1 x 2
##   region       n
##   <chr>    <dbl>
## 1 SSC22015 37948

6.1 Scatter Plot: Ratio of old to young vs population

## [1] "1"

1. When the population is low, the ratio of old to young is high. This suggests that there are more old people than young people when the population of a region is low.

2. When the population is high, the ratio is low. This shows that in the more populous regions, there are more young people than old people.

3. This is consistent with a trend that older people would move to a small country town where the cost of housing is cheaper, and they will have a greater spending power with their limited funds and many of the people are likely retired.

4. The younger couples and people will live in a more populous region for cheaper housing, jobs, schooling, health facility and other conveniences to support their lifestyles.

5. There are many more in between the two extremes, and the trend will depend on a combination of factors. e.g life stages, wealth levels, empty nesters, availability of jobs etc.


7.1 Scatter Plot: Ratio of female to male vs population

## [1] "1"
## [1] 5.3333
## [1] 0

1. In regions where the population is low, the ratio of female/male ranges from very low to a high of 5.33.

3. Another possible reason for the high ratio could be that the male of the family who are still fit and healthy to work, will go to more populous regions to find work and send money home. This way the female members could stay put in a region where cost of living is lower, and rely on the income earned by the male members of the family. e.g. This is quite typical in countries like china, where the male members will go from rural villages to the big city to earn an income to support their families in the poor villages.

8.1

Females 18 to 21 have been chosen as the primary customers for the hypothetical product of a face cream that will make a young woman look even more beautiful. In addition, the purchaser of the product has a chance of referring other customers to buy the product. The top three referrers will earn a free dinner for two in a five star restaurant.

8.2

1. The two regions with the largest population of females between 18 and 21 are SSC22015 (1113) and SSC20492 (2566).

2. Females between 18 to 21 are young, impulsive, vulnerable and usually very active in the social media. By targeting the two regions with the highest number of young female in this age group, the multiplying effect will be the greatest when the new product is launched, and increasing the chance of achieving the greatest sales volume in the regions, as well as influencing the sales in other regions through the social media.


Question 9 Comment

The four plots in 9.3 show that as n increases, the sample distribution approaches the normal distribution, confiming CLT which states that the distribution of sample means of any distribution will tend to the normal distribution. (Math2406, Applied Analytic 3.20)

Reference

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