1. Warm – Up
Find the Mean, Median, Mode, IQR and Standard Deviation of the age of a room containing 5 people. Ages: 16, 18, 17, 16, 19.
Calculate all values a second time. Describe what happens to these values if someone’s 99 year old Grandma walks into the room.
Mean =
Mode =
Median =
Standard Dev. =
IQR =
17.2 16 17
1.304
2.5
Mean =
Mode =
Median =
Standard Dev. =
IQR =
30.833 16
17.5
33.415 3

2. CHAPTER 5 (continued)
The Mean and the Std. Dev. are considered NONRESISTANT because they’re very sensitive and influenced by extreme outliers.
The Median, IQR, and Mode are considered RESISTANT or ROBUST, since outliers do not ‘greatly’ (if at all) affect their value.

3. The Mean in relation to the Median
CHAPTER 5 (continued)
The Mean in relation to the Median
If the Mean is (roughly) equal to the Median then the distribution is approximately symmetric.
If the Mean is greater than the Median then the distribution is skewed right.
If the Mean is less than the Median then the distribution is skewed left.
A = Mode
B = Median
C = Mean
A = Mode
A = Median
A = Mean
C = Mode
B = Median
A = Mean

4. Unbiased – Statistics are unbiased when the center of the distribution is approximately equal to the true population average.
Biased True population mean.
Unbiased and small spread are the best.
You can generalized only if the data was RANDOMLY collected from entire population.

5. The Five Number Summary: Minimum, Q1, Median, Q3, Maximum
The Five Number Summary can be displayed in a BOX PLOT (A Box and Whisker Plot)
Min. Q Med Q3 Max.

6. Babe Ruth’s # of Home Runs with the New York Yankees 1920-1934
Calculate the Mean, Standard Deviation, and 5-Number summary. Then constructing a Box Plot with the following data:
Babe Ruth’s # of Home Runs with
the New York Yankees
Mean =
Standard Dev. =
Min = 22, Q1 = 35
Median = 46
Q3 = 54, Max = 60 22
Min. 35 Q1 46
Med. 54 Q3 60
Max.
# of Ruth’s Home Runs

7. What is an OUTLIER ?

8. Formula to Determine Outliers: An Observation, xi , is an Outlier if:
xi > Q (IQR) or
xi < Q1 – 1.5(IQR)
Determine if any Outliers exist for
#H.Runs:
Xi > Q ∙(IQR) =
Xi > (54 – 35) = 82.5
Xi < Q ∙(IQR) =
Xi < (54 – 35) = 6.5
Q1 = 35
Q3 = 54
IQR = 19

9. HW: #4, 15, 17 on REVIEW sheet.

10. HW: Page 92:14, 16, 22
22.

12. HW: Page 92:14, 16, 22

13. HW: Page 92:14-24 even March/April February July
The Med. for June is higher and more consistent than Jan.
Summer months have more consistent temp.

14. The Modified Box Plot represents Outliers outside of the Box Plot.

15. Example of Box Plot for Multiple data Sets
Heights of Plant (mm)