MultiAngle is a NSW-based business specialised in providing tailor-made travel insurance. The CEO is assessing MultiAngle’s investment in three platforms where its advertisement runs: social media, TV and radio. The following table shows the descriptive statistics of profit per month (dollars in thousands) generated from TV and radio advertisement, based on 12 monthly profit figures in a randomly chosen year. Platform Mean Variance Social Media X X TV 12.8 11.23 Radio 6.5 0.93 The analyst hired by MultiAngle lost her result of social media by accident. Fortunately, she managed to recover the raw data of monthly profit figures for s ocial media, as shown in the table below. Monthly profit generated through social media advertisement, sorted ascending order Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 1.8 9.6 3.5 19.3 19.9 11.9 24.5 1.2 13.5 14.8 2.9 4.9 (i) Does the data correspond to the population or a sample? (ii) Find the median of monthly profit generated by social media advertisement (iii) Compute the mean profit generated by social media advertisement (iv) Compute the variance and standard deviation for social media advertisement (v) Relative to each platform’s mean return achieved, which option generates the greatest volatility in profit? (Hint: Use CV) Only answer (iv) and (v)
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
MultiAngle is a NSW-based business specialised in providing tailor-made travel insurance. The CEO is assessing MultiAngle’s investment in three platforms where its advertisement runs: social media, TV and radio. The following table shows the
|
Platform |
Mean |
Variance |
|
Social Media |
X |
X |
|
TV |
12.8 |
11.23 |
|
Radio |
6.5 |
0.93 |
The analyst hired by MultiAngle lost her result of social media by accident. Fortunately, she managed to recover the raw data of monthly profit figures for s ocial media, as shown in the table below.
|
Monthly profit generated through social media advertisement, sorted ascending order |
||||||||||||
|
Jan |
Feb |
Mar |
Apr |
May |
Jun |
Jul |
Aug |
Sep |
Oct |
Nov |
Dec |
|
|
1.8 |
9.6 |
3.5 |
19.3 |
19.9 |
11.9 |
24.5 |
1.2 |
13.5 |
14.8 |
2.9 |
4.9 |
|
(i) Does the data correspond to the population or a sample?
(ii) Find the median of monthly profit generated by social media advertisement
(iii) Compute the mean profit generated by social media advertisement
(iv) Compute the variance and standard deviation for social media advertisement
(v) Relative to each platform’s mean return achieved, which option generates the greatest volatility in profit? (Hint: Use CV)
Only answer (iv) and (v)
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