# A Comprehensive Statistical Report on Employee Salaries at InoSmart Inc.

This Statistical Analysis assignment required a meticulous examination of twelve months' worth of aggregate salary data, scrutinizing aspects such as the mean, median, standard deviation, and skewness of the salary distribution. The report reveals crucial information for the company's General Manager and stakeholders, shedding light on the central tendencies, variability, and distribution of salaries. The results presented here offer a clear picture of the company's salary structure, enabling data-driven decision-making for InoSmart Inc.'s leadership.

## Problem Description:

As the newly appointed Economic Advisor for InoSmart Inc., you have been tasked with providing an analysis of the salaries paid to the company's employees in the previous year. The General Manager of the company has requested insights into the nature of these salaries. The Chief Accountant has provided you with the aggregate monthly salary data, and your goal is to summarize this data in a Word document chart and draw statistical conclusions based on your analysis, performed using Microsoft Excel Data Analysis Toolpak.

## Solution

Analysis and Findings:

The data provided consists of twelve months of aggregate salary information, offering valuable insights into the company's payroll structure. Here are the key findings based on the analysis:

Summary of Descriptive Statistics:

Table 1 below provides an overview of the descriptive statistics calculated for the aggregate salaries:

Metric Value
Mean \$648,908.33
Median \$748,400
Standard Deviation \$273,342.33
Skewness -1.98
Range \$748,600
Minimum \$67,950
Maximum \$816,550
Sample Size 12

Mean Calculation:

The mean average salary was calculated by summing the aggregate salaries for all twelve months and then dividing this sum by the number of observations:

Mean Average Salaries = (743,430 + 705,320 + ... + 805,500) / 12 = \$648,908.33

Standard Deviation:

The standard deviation (SD) was calculated as follows:

SD = √((∑(Average Salaries - Mean Average Salaries)²) / 12) = \$273,342.33

Median Calculation:

The median is the central value when the data is ordered in increasing order. The values in positions 6 and 7 were averaged to calculate the median:

Median = (743,430 + 753,370) / 2 = \$748,400

Range Calculation:

The range of the variable was calculated as the difference between the maximum and minimum values:

Range = Maximum - Minimum = \$816,550 - \$67,950 = \$748,600

## Conclusions:

InoSmart Inc.'s employee salary analysis reveals the following:

• The range of aggregate salary values extends from a minimum of \$67,950 to a maximum of \$816,550, resulting in a range of \$748,600.
• The average aggregate salary for the period analyzed is approximately \$648,908.33, with a standard deviation of \$273,342.33. This suggests some variation in salaries over the year.
• The median salary, representing the middle value when ordered, is \$748,400. This means that 50% of the months had aggregate salaries less than or equal to this amount.
• The distribution of aggregate salaries exhibits negative skewness, indicating a bias towards lower values. This suggests the possibility of outliers among lower salary values, which should be further investigated.

## Appendix: Collected Data:

Here is the detailed data for each month's aggregate salaries:

Month Aggregate Salaries
January \$743,430
February \$705,320
March \$67,950
April \$780,240
May \$801,970
June \$69,440
July \$816,550
August \$734,380
September \$791,110
October \$753,370
November \$717,640
December \$805,500

These findings provide valuable insights into the nature of salaries paid by InoSmart Inc., enabling informed decision-making for the company's management.