Variance and Standard Deviation IB Math SL Chapter 20F

20F.1 Variance and Standard Deviation Another way to discuss spread of data Range and IQR only use two values of data, so we need a better way to describe the spread.

Variance

Standard Deviation Standard deviation is only useful if the distribution is approximately symmetrical. Most useful if data is normally distributed (CH 24). Standard deviation is quoted more than variance. IQR and percentiles are more appropriate tools for measuring spread if distribution is skewed.

Example 6 p.518

Answers

Using Technology Enter data into graphing calculator list. STAT, edit 1, clear L1 by moving curser on top of L1 and hit clear enter, enter data, 2nd quit. Run 1-variable test STAT, CALC, 1-Var Stats, 2nd 1 to get L1, enter “1-Var Stats L1”

Using technology What does all this mean?

Another Super fun example

Another Super fun example Answer:

20F.2 Sampling from a population Populations are often too large to gather all data. Thus, a random sample is taken from the population in hopes it truly reflects characteristics of the population. Samples must be large and unbiased.

Notations

20F.3 Standard deviation for group data FYI: For continuous data, or data that has been grouped in classes, we use the midpoint of the interval to represent all data in that interval.

Example:

Example: