Question

Describe what a standard deviation is conceptually. How would you use it in your daily life or in your job now? Please provide short examples.

Answer 1

Answer:

Standard Deviation :

Standard deviation is a measurement used in statistics of the amount a number varies from the average number in a series of numbers. The standard deviation tells those interpreting the data, how reliable the data is or how much difference there is between the pieces of data by showing how close to the average all of the data is.

• A low standard deviation means that the data is very closely related to the average, thus very reliable.
• A high standard deviation means that there is a large variance between the data and the statistical average, thus not as reliable.

Formula:

The formula for standard deviation is

Sample Standard Deviation =

Where:

x_i = Value of the i^th point in the data set

= The mean value of the data set

n = The number of data points in the dataset

Real Life Examples:

• A class of students took a math test. Their teacher found that the mean score on the test was an 85%. She then calculated the standard deviation of the other test scores and found a very small standard deviation which suggested that most students scored very close to 85%.
• An employer wants to determine if the salaries in one department seem fair for all employees, or if there is a great disparity. He finds the average of the salaries in that department and then calculates the variance, and then the standard deviation. The employer finds that the standard deviation is slightly higher than he expected, so he examines the data further and finds that while most employees fall within a similar pay bracket, three loyal employees who have been in the department for 20 years or more, far longer than the others, are making far more due to their longevity with the company. Doing the analysis helped the employer to understand the range of salaries of the people in the department.