Standard Deviation

Step 1

STEP 1 - MEAN Calculate the mean

Step 2

STEP 2 - DEVIATIONS Calculate the deviation from the mean for each value in the distribution

Step 3

STEP 3 - SQUARE Square each deviation calculated in Step 2

Step 4

STEP 4 - ADD Add all of the squared deviations in Step 3

Step 5

STEP 5 - DIVIDE Divide the Sum in Step 4 by the total number - 1 Sum --------- Total - 1

Step 6

STEP 6 - SQUARE ROOT Square root the final value in Step 5 sqrt ( Sum ) . --------- . Total - 1

Standard Deviation (SD) is a measure of variability calculated using deviations from the _______. (a) mean (b) mode (c) median

(a) mean Standard Deviation (SD) is a measure of variability calculated using deviations from the MEAN.

In terms of athletes, the observed value is the athlete's _________ and the mean is the athlete's _________. (a) team, opponent (b) performance, ability (c) ability, performance

(b) In terms of athletes, the observed value is the athlete's performance and the mean is the athlete's ability. Observed value of an athlete - performance Mean value of an athlete - ability The standard deviation measures the distance between an athlete's PERFORMANCE and his/her ABILITY. Performance = ability + random chance

Just by looking at 2 graphs, how can you tell which one has the greater standard deviation? What is one way you can tell?

A larger spread will result in a larger standard deviation. If the range is much bigger, there are greater differences.

Definition of Standard Deviation

A measure of how spread out numbers are. A measure of how much deviation there is from the mean. A measure of difference between an observed value and the mean.

Break it down What does DEVIATION mean?

Deviation is the act of departing from a set standard. "How far away from the mean"

Interpret this example: Semester 1. Dom takes quizzes every month (Aug-Dec). His average quiz score is 90%. In November, he scored a 60% on all of his quizzes. The standard deviation is 25%.

Over the first semester, Dom's November performances were typically about 25% from his ability.

What words need to be used to form your answer into a sentence?

PERFORMANCE TYPICALLY VARY ABILITY

Ability represents...

The Mean

Performance represents...

The observed values

Standard Deviation definition from the book

The standard deviation measures the variability (spread) in a distribution using the squared deviations from the mean.