Download 12.6 Statistical Measures

12.6 Statistical Measures
Vocabulary
• Measure of central tendency: one number that
describes a set of data
USE
WHEN…
Mean (𝑋)
The data are spread out and you want an
average (add all and divide by total # of items)
Median
The data contains outliers (put all in order from
Mode
The data are tightly clustered around one or
two values (the #s that appear the most often)
least to greatest and find the exact middle number)
Example
• Find the mean, median, and mode given the set of data:
{1, 2, 2, 3, 3, 3, 4, 4, 5}
{-1, 5, 2, 2, 10, 2, -2, 4, 5}
Choosing a Central Tendency
• A sweepstakes offers a first prize of $10,000, two second prizes of $100,
and one hundred third prizes of $10. Which measure of central tendency
best represents the available prizes?
• Mode or median
• Which measure of central tendency would the organizers of the
sweepstakes be most likely to use in their advertising?
• Mean b/c it will trick people to think that they have a chance to win more
money, even though there are only 3 prizes above $10
Measures of Variation (dispersion)
• Measure how spread out or scattered a set of
data is
– Simplest measure of variation to calculate is the
range ( Highest value – Lowest value)
• Variance and Standard deviation: measures of
variation that indicate how much the data
values differ from the mean
To find variance (σ2)
1. Find the mean ( 𝑋 )
2. Then use the following formula.
2 +(𝑥 −𝑋)2 +(𝑥 −𝑋)2 +………+(𝑥 −𝑋)2
(𝑥
−𝑋)
1
2
3
𝑛
Variance (σ2)=
𝑛
Standard Deviation(σ) =
(𝑥1 −𝑋)2 +(𝑥2 −𝑋)2 +(𝑥3 −𝑋)2 + ……..+(𝑥𝑛 −𝑋)2
𝑛
Using the calculator to find the
variance and standard deviation
1.
2.
3.
4.
5.
6.
7.
8.
Hit stat
Select edit
Input entries into one of the lists (L1, L2, …)
Exit out
Hit stat
Select the calc menu
Select 1- var stats hit enter
Then hit 2nd and select the list you want to
find the standard deviation. Hit enter
9. Look for the σx this is the standard deviation
Example
• The leading number of home runs in Major League Baseball for the 19992004 seasons were 50, 73, 57, 47, and 48. Find the variance and standard
deviation of the data to the nearest tenth.
Example 2
• The following list shows the rebounding totals for the members of a local
basketball team: 162, 145, 179, 37, 44, 53, 70, 65, 47, 35, 71, 5, 5. Find the
variance and standard deviation.