The two selected variables from the collected data are age group (question 1) and the annual income (question 2). Descriptive statistics, namely, the mean, mode, median, variance, and standard deviation, were used to analyze data of each of the selected variable. Moreover, the probability of the occurrence of every event in each of the two variables was determined.
The Mean, Mode, and Median of the Age Group and the Level of Annual Income
The Level of Age Groups of Customers
Table 1.
Mean = ∑fx/∑f = 1089/30 (Carlberg, 2014).
Modal class = 18-30
Low boundary = 17.5
Frequency before modal class = 0
Frequency of modal class = 15
Frequency after modal class = 8
Width of the modal class = 13
Mode = 17.5 + (15-0)/[(15-0)+ (15-13)] * 13 = 17.5 + (15)/(15 + 2) * 13 = 17.5 + (15/17) * 13 = 17.5 +(0.882 * 13) = 17.5 + 11.466 = 28.966
Median
Lower class boundary = 17.5
n = 30
Cumulative f before = 0
Frequency of median group = 15
Width of the group = 13
Median = 17.5 + [(30/2 – 0)/15] * 13 = 17.5 + (15/15)*13 = 17.5 + 13
The Level of Annual Income
Table 2.
Mean = 87/30 = 2.9
Modal class = 2-3 (average)
Lower boundary = 2.5
Frequency before modal class = 5
Frequency of modal class= 16
Frequency after modal class = 4
Width of modal class = 1
Mode = 2.5 + (16-5)/[(16-5)+ (16-4)] * 1 = 2.5 + (11)/(11 + 12) * 1 = 2.5 + (11/23) * 1 = 2.5 +(0.478 * 1) = 2.5 + 0.47 = 2.978
Median
Lower class boundary = 2.5
N = 30
Cumulative frequency before = 8
Frequency of median group = 16
Width of the group 1
Median = 2.5 + [(30/2 – 8)/16] * 1 = 2.5 + (7/16)*1 = 2.5 + 0.438 = 2.938
The Determination of Variance of the Age Group and the Level of Annual Income
The Age Group of Customers
Table 3.
Variance = ∑(x-mean)^2/n) = 2342.76/30 = 78.092
Table 4.
Variance =∑(x-mean)^2/n) = 10.05/30 = 0.335
Standard Deviation of the Age Group and the Level of Annual Income
Standard deviation of age group = [∑(x-mean)^2/n)]^0.5 (Brase & Brase, 2017) = [2342.76/30] = 78.092^0.5 = 8.837
Standard deviation of the level of income = [∑(x-mean)^2/n)]^0.5 (Jani, 2014) = [10.05/30]^0.8 = 0.335^0.5 = 0.579
The Probability of Each Event in Age Group and the Annual Income Level
Table 5.
Table 6.
References
Brase, C. H., & Brase, C. P. (2017). Understandable statistics: Concepts and methods. New York, NY: Brooke/Cole.
Carlberg, C. G. (2014). Statistical analysis: Microsoft Excel 2013. Indianapolis, IN: Que.
Jani, P. N. (2014). Business statistics: Theory and applications. New York, NY: PHI Learning.