Math 2311 Bekki George – [email protected] Office Hours: MW 11am to 12:45pm in 639 PGH Online Thursdays 4-5:30pm And by appointment Class webpage:

Math 2311 Class Notes for Section 1.3 - 1.5 Section 1.3: Another important question we want to answer about data is about its spread or dispersion. Roughlyspeaking, the population standard deviation, σ, tells the average distance that data values fall from the mean. The standard deviation is the square root of the population variance, σ2. So, what is the variance? The variance is the average of the squared differences of the data values from the

x

σ2

Most of the time we are not working with the entire population. Instead, we are working with a sample. •Sample variance - s2=(xi−x)i=1n∑n−1•Sample standard deviation - s=s2Example: 1. A statistics teacher wants to decide whether or not to curve an exam. From her class of 300 students, she chose a sample of 10 students and their grades were: 72, 88, 85, 81, 60, 54, 70, 72, Find the mean, variance and standard deviation for this sample. 63, 43

2. Suppose the statistics teacher decides to curve the grades by adding 10 points to each score. What is the new mean, variance and standard deviation?