Usual and Unusual Values
(Normal Distribution)
(Section 11-3 Alg 2)
Essential Question: What makes a value “unusual” statistically speaking?
Students will write a summary discussing unusual statistical values.
.
Outlier is a value that is much greater than or much less than most of the other
values in a data set.
An outlier can significantly affect the mean and standard deviation making our
picture of the data misleading.
If a value is more than 2 standard deviations above or below the mean, it is
considered “unusual”.
Therefore the minimum “usual” value is mean – 2 standard deviations or x  2
and the maximum usual value is mean + 2 standard deviations or x  2
Essential Question: What makes a value “unusual” statistically speaking?
Students will write a summary discussing unusual statistical values.
Example 1: Given the data set and values below, verify that 65 is an outlier.
Data set: 65, 173, 181, 184, 188, 190, 192, 199
Mean: 171.5
Standard Deviation: 40.899
Essential Question: What makes a value “unusual” statistically speaking?
Students will write a summary discussing unusual statistical values.
Full data set
without 65
Mean: 1372//8 = 171.5
Median: (184+188)/2 = 186
Mode: none
Standard deviation:
Mean: 1307/7 = 186.71
Median: 188
Mode: None
Standard deviation:
65
-106.5
11342.35
173
-13.71
187.9641
73
1.5
2.25
181
-5.71
32.6041
181
9.5
90.25
184
-2.71
7.3441
184
12.5
156.25
188
1.29
1.6641
188
16.5
272.25
190
3.29
10.8241
190
18.5
342.25
192
5.29
27.9841
192
20.5
420.25
199
12.29
151.0441
199
27.5
756.25
Total =
1372
Total =
13382
𝑥 = 171.5
𝜎=
13382
8
Total = 1307
Total =
419.4287
𝑥 = 186.71
𝜎=
419.4287
7
Essential
Question: What makes a value “unusual” statistically
speaking?
= 40.899
= 7.741
Students will write a summary discussing unusual statistical values.
Essential Question: What makes a value “unusual” statistically speaking?
Students will write a summary discussing unusual statistical values.
Essential Question: What makes a value “unusual” statistically speaking?
Students will write a summary discussing unusual statistical values.
2
3
Essential Question: What makes a value “unusual” statistically speaking?
Students will write a summary discussing unusual statistical values.
4
5
Essential Question: What makes a value “unusual” statistically speaking?
Students will write a summary discussing unusual statistical values.
6
7
Essential Question: What makes a value “unusual” statistically speaking?
Students will write a summary discussing unusual statistical values.
8
Essential Question: What makes a value “unusual” statistically speaking?
Students will write a summary discussing unusual statistical values.
9
Essential Question: What makes a value “unusual” statistically speaking?
Students will write a summary discussing unusual statistical values.
10
Essential Question: What makes a value “unusual” statistically speaking?
Students will write a summary discussing unusual statistical values.
11
Essential Question: What makes a value “unusual” statistically speaking?
Students will write a summary discussing unusual statistical values.
HW #___ Practice 11-3
Essential Question: What makes a value “unusual” statistically speaking?
Students will write a summary discussing unusual statistical values.