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Data Analysis Report

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Updated: May 28th, 2021

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.

Q1: Age groups
Age groups Lower limit Upper limit Mid-Point (x) Frequency fx
18-30 17.5 30.5 24 15 360
30-45 30.5 45.5 38 8 304
45-60 45.5 60.5 53 5 265
60+ 60 100 80 2 160
30 1089

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.

Q2: Levels of annual income.
Class interval Lower limit Upper limit Mid-point (x) Frequency (f) fx
Very high 4-5 4.5 5.5 5 2 10
High 3.5 3.5 4.5 4 4 16
Average 2-3 2.5 3.5 3 16 48
Low 1-2 1.5 2.5 2 5 10
Very Low 0-1 0.5 1.5 1 3 3
30 87

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.

Q2: Age group.
Age group Mid-Point (x) Frequency fx (x-mean) (x-mean)^2
18-30 24 15 360 -12.3 151.29
30-45 38 8 304 1.7 2.89
45-60 53 5 265 16.7 278.89
60+ 80 2 160 43.7 1909.69
30 1089 2342.76

Variance = ∑(x-mean)^2/n) = 2342.76/30 = 78.092

Table 4.

Q2: The level of annual income.
Class interval Lower limit Upper limit Mid-point (x) Frequency (f) fx (x-mean) (x-mean)^2
Very high 4-5 4.5 5.5 5 2 10 2.1 4.41
High 3.5 3.5 4.5 4 4 16 1.1 1.21
Average 2-3 2.5 3.5 3 16 48 0.1 0.01
Low 1-2 1.5 2.5 2 5 10 -0.9 0.81
Very Low 0-1 0.5 1.5 1 3 3 -1.9 3.61
30 87 10.05

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.

Probability of a customer occurring in each age group
Age group Frequency Probability
18-30 15 0.50
30-45 8 0.27
45-60 5 0.17
60+ 2 0.07
30 1.00

Table 6.

The Probability of a customer occurring in each of the annual income level
Class interval Frequency (f) Probability
Very high 4-5 2 0.07
High 3.5 4 0.13
Average 2-3 16 0.53
Low 1-2 5 0.17
Very Low 0-1 3 0.10
30 1.00

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.

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