# STA 1063C Lecture Notes - Lecture 10: Standard Deviation, Descriptive Statistics, Summary Statistics

For unlimited access to Class Notes, a Class+ subscription is required.

Shapes of Distributions

o Symmetric: same on either side of the highest point in the middle (bell curve)

o Uniform: all observations occur the same amount of times

In symmetric data, mean=median

o Skewed right- most data is over to the left of the graph

Mean > median

o Skewed left- most data is over to the right of the graph

Mean < median

o Example: how will the following data sets be distributed?

A. Grades on an easy test- skewed left, mean < median

B. Grades on a difficult test- skewed right, mean > median

C. Number of days spent in the hospital last year- skewed right, mean >

median

D. Scores on SAT/ACT- symmetric, mean=median

Measures of variation

o Range: max-min

o The deviation for each value x is the difference between the value of x and the

mean of the data set

Example: 4, 6, 11

Mean: 7

4-7= -3; 6-7= -1; 11-7= 4

Deviation always adds to be 0; need a different measure of variation

o Squares of deviations

sum of (x-mu) squared/N --N= population size

Note: units are squared

Standard Deviation: square root of the variance

sum of (x-xbar) squared/n-1 –n= sample size

Example: (-3)sq. + (-1)sq. + (4)sq./2

S sq. = 13

Square root of 13= 3.61 (standard deviation)

The more spread the data set, the larger the standard deviation

If all your observations are the same, there will be no variation or standard

deviation (0)

Standard deviation is always greater than or equal to zero (positive)

Distributions on Excel

o Open new workbook and enter data

Label column A “data”

o Data tab > data analysis > descriptive statistics > select all data for input range >

new worksheet ply > select summary statistics

o Enlarge column by double clicking between A and B

o Go back to data sheet, enter deviations – Use mean from descriptive statistics

Label column B “deviations”

find more resources at oneclass.com

find more resources at oneclass.com