Descriptive Data Statistics: Calculating the Probability Report

Exclusively available on IvyPanda Available only on IvyPanda

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.

We will write a custom essay on your topic a custom Report on Descriptive Data Statistics: Calculating the Probability
808 writers online

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 groupsLower limitUpper limitMid-Point (x)Frequencyfx
18-3017.530.52415360
30-4530.545.5388304
45-6045.560.5535265
60+60100802160
301089

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

1 hour!
The minimum time our certified writers need to deliver a 100% original paper

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

Remember! This is just a sample
You can get your custom paper by one of our expert writers

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 intervalLower limitUpper limitMid-point (x)Frequency (f)fx
Very high4-54.55.55210
High3.53.54.54416
Average2-32.53.531648
Low1-21.52.52510
Very Low0-10.51.5133
3087

Mean = 87/30 = 2.9

Modal class = 2-3 (average)

Lower boundary = 2.5

Frequency before modal class = 5

We will write
a custom essay
specifically for you
Get your first paper with
15% OFF

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 groupMid-Point (x)Frequencyfx(x-mean)(x-mean)^2
18-302415360-12.3151.29
30-453883041.72.89
45-6053526516.7278.89
60+80216043.71909.69
3010892342.76

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

Table 4.

Q2: The level of annual income.
Class intervalLower limitUpper limitMid-point (x)Frequency (f)fx(x-mean)(x-mean)^2
Very high4-54.55.552102.14.41
High3.53.54.544161.11.21
Average2-32.53.5316480.10.01
Low1-21.52.52510-0.90.81
Very Low0-10.51.5133-1.93.61
308710.05

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 groupFrequencyProbability
18-30150.50
30-4580.27
45-6050.17
60+20.07
301.00

Table 6.

The Probability of a customer occurring in each of the annual income level
Class intervalFrequency (f)Probability
Very high4-520.07
High3.540.13
Average2-3160.53
Low1-250.17
Very Low0-130.10
301.00

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.

Print
Need an custom research paper on Descriptive Data Statistics: Calculating the Probability written from scratch by a professional specifically for you?
808 writers online
Cite This paper
Select a referencing style:

Reference

IvyPanda. (2022, May 10). Descriptive Data Statistics: Calculating the Probability. https://ivypanda.com/essays/data-analysis/

Work Cited

"Descriptive Data Statistics: Calculating the Probability." IvyPanda, 10 May 2022, ivypanda.com/essays/data-analysis/.

References

IvyPanda. (2022) 'Descriptive Data Statistics: Calculating the Probability'. 10 May.

References

IvyPanda. 2022. "Descriptive Data Statistics: Calculating the Probability." May 10, 2022. https://ivypanda.com/essays/data-analysis/.

1. IvyPanda. "Descriptive Data Statistics: Calculating the Probability." May 10, 2022. https://ivypanda.com/essays/data-analysis/.


Bibliography


IvyPanda. "Descriptive Data Statistics: Calculating the Probability." May 10, 2022. https://ivypanda.com/essays/data-analysis/.

Powered by CiteTotal, best reference maker
If you are the copyright owner of this paper and no longer wish to have your work published on IvyPanda. Request the removal
More related papers
Cite
Print
1 / 1