1. 11.1 Find Measures of Central Tendency & Dispersion
Algebra II

2. An intro to Statistics
Statistics – numerical values used to summarize & compare sets of data (such as ERA in baseball).
Measures of Central Tendency – mean, median, & mode are the 3 we will be using. Tells you what the “center” of the data is.

3. Mean – ( x ) average of n numbers (add all #s & divide by n)
Median – the middle # when the #s are written in order from least to greatest or greatest to least. If there are 2 middle numbers, the median will be the average of those 2.
Mode – the number(s) that occur most frequently. It is possible to have more than 1 mode or even no mode.

4. Median – Put the numbers in order first!
Ex. 1: Find the mean, median, & mode of the following set of numbers: 36, 39, 40, 34, 48, 33, 25, 30, 37, 17, 42, 40, 24.
Mean 13
Median – Put the numbers in order first!
17, 24, 25, 30, 33, 34, 36, 37, 39, 40, 40, 42, 48
Mode – most frequent!
40 is the mode.

5. Measures of Dispersion – tell how spread out the data are.
* Range – Difference between the largest and smallest values.
(for example: the range of the last example would be 48-17=31)
* Standard Deviation - (σ – “sigma”)
x is the mean
x1, x2, x3, …, xn are the entries in the data set.
n is the number of entries in the set

6. Ex 2: Find the standard deviation of the data from the first example

7. assignment

8. Hints for making a box-and-whiskers plot:
Make sure data is in order from least to greatest.
Find the minimum value, median, maximum value, upper & lower quartiles
17, 24, 25, 30, 33, 34, 36, 37, 39, 40, 40, 42, 48
Plot the points for this info below a number line.
Draw the box and whiskers.

9. Box-and-whisker plots
Minimum value (17)
Maximum value (48)
Median (36)
Lower Quartile – median of all numbers in the list to the left of the median
(25+30)/2 = 27.5
Upper Quartile – median of all numbers to the right of the median
(40+40)/2 = 40

10. Frequency Distribution
Count the number of tally marks and put the total in the last column.
Assign appropriate intervals that will include all data values in the set.
Put a tally mark for each data value in the appropriate row.
Title Goes Here
Interval
Tally
Frequency
0 to 9
10 to 19  l 1
20 to 29
 ll 2
30 to 39
 llll l 6
40 to 49
 llll 4

11. Another way to show the same info. is in a histogram.
Frequency
TITLE HERE
Bars should be touching!
L A B E L
H E R E 6 5 4 3 2 1
0 - 9
Intervals
LABEL HERE

12. Assignment