1. Measures of Central Tendency
Statistics
Measures of Central Tendency

2. A statistician with her feet in a fire and her head in covered in ice will say that, on average, she feels fine.
Statistics tries to organize and understand numerical information.
Example: If we asked everyone in the class how many cans of soda they drank in a day we would end up with a list of numbers:
2, 4, 1, 1, 2, 3, 0, 1, 6, 3, 2, 2, 2, 1, 0, 1, 3, 2, 1.
Statistics gives us tools to help us understand this group of numbers.
Each number is a data value and the whole group together is the sample data.

3. Ways to analyze data:
Mean, median and mode are measures of central tendency – values that describe the center of a data set.
The mean is the sum of the values in the set divided by the number of values
𝑥 = 𝑥 𝑛
The median is the middle value or the average of the two middle values if there is an even number of data values.
The mode is the value or values that occur most often. A data set might have one mode, no mode or several modes.
Ex: Sodas drank in a day: 2, 4, 1, 2, 2, 3, 0, 1, 5, 3, 2, 2, 2, 1, 0, 1, 3, 2, 1, 4.
Mean:
Median:
Mode:

4. 𝑤𝑒𝑖𝑔ℎ𝑡𝑒𝑑 𝑎𝑣𝑒𝑟𝑎𝑔𝑒= 0 2 +5 1 +7 2 +3 3 +1 4 +1(5) 2+5+7+3+2+1
Weighted Average: is a mean calculated by using frequencies of data values.
Sodas drank in a day: 2, 4, 1, 2, 2, 3, 0, 1, 5, 3, 2, 2, 2, 1, 0, 1, 3, 2, 1, 4
Cans of Soda 1 2 3 4 5
Frequency
𝑤𝑒𝑖𝑔ℎ𝑡𝑒𝑑 𝑎𝑣𝑒𝑟𝑎𝑔𝑒= (5)
𝑤𝑒𝑖𝑔ℎ𝑡𝑒𝑑 𝑎𝑣𝑒𝑟𝑎𝑔𝑒=
𝑤𝑒𝑖𝑔ℎ𝑡𝑒𝑑 𝑎𝑣𝑒𝑟𝑎𝑔𝑒= =1.85 ≈2

5. Expected Value: is the weighted average for a data sample
Expected Value: is the weighted average for a data sample. If we randomly asked a student how many cans of soda they drank, we would expect their answer to be 2.
Cans of Soda 1 2 3 4 5
Probability
2 20
5 20
7 20
3 20
1 20
𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑣𝑎𝑙𝑢𝑒=
𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑣𝑎𝑙𝑢𝑒=
𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑣𝑎𝑙𝑢𝑒= =2.1

6. Box and whisker plots: shows the spread of a data ser
Box and whisker plots: shows the spread of a data ser. It displays 5 key points: the minimum and maximum values, the median, and the first and third quartiles (Q1 and Q2).
The interquartile range (IQR) is the difference between Q1 and Q3, or Q3-Q1. It represents the middle 50% of the data.
Quartile 1 is the median value of the first half of the data.
Quartile 3 is the median value of the second half of the data.

7. Sodas drank in a day: 2, 4, 1, 2, 2, 3, 0, 1, 5, 3, 2, 2, 2, 1, 0, 1, 3, 2, 1, 4
0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 5 5

8. TI 83/84 Calculator Input – Box and Whisker
Step 1) Entering data into List
STAT  Enter (Edit…) Enter data into L1 (or other L)
Step 2) Create box and whisker plot
2nd  Y= (STAT PLOT)  Enter (1: Plot 1)
 Enter (to turn on plot)  Down, Right, Right, Right, Right
(2nd level, center picture)  Enter  Down (enter list number)
Step 3) Viewing box and whisker plot
Zoom  #9 (ZoomStat)  Graph
Step 4) Finding Min, Max, Q1, Q2 and Median
Trace  left and right buttons to view entries

9. TI 83/84 Calculator Input – Statistics
Step 1) Entering data into List
STAT  Enter (Edit…) Enter data into L1 (or other L)
Step 2) View Statistics
STAT  right (CALC)  Enter (1: 1-Var Stats)  Enter
Scroll down to see:
n = sample size
minX = minimum value
Q1 = quartile 1
Med = Median value
Q3 = quartile 3
maxX = maximum value