1. 11.1 Measures of Center and Variation

2. What We Will Learn Compare mean, median, and mode
Find range and standard deviation
Identify effects of transformations on data

3. Needed Vocab Measure of center: mean, median, and mode
Mean: sum of the data divided by total number of data values, aka average
Median: middle number when values written in order
Mode: value or values that occur the most
Outlier: data value much larger or smaller than the other values
Measure of variation: describes the spread or distribution
Range: difference of greatest value and least value
Standard deviation: how much a value in the data set differs from the mean
Data transformation: use a mathematical operation to change a data set into different data set

4. Ex. 1 Comparing Measures of Center
Aka Measures of Central Tendency
A. Find mean, median, and mode
B. Which measure best represents the data?
Mean = 9.65
Median = 8.7
Remember to write in numerical value to find median, if even number the add middle two and divide by 2
Mode = 8.25
Median - as mean bigger than most data values, and modes less than most data values
Hourly
Wages
16.50
8.25
8.75
8.45
8.65
9.10
9.25

5. Ex. 2 Removing an Outlier
Hourly
Wages
16.50
8.25
8.75
8.45
8.65
9.10
9.25
How does outlier affect the mean, median, and mode?
Run mean, median, and mode with outlier and then run without and see difference
With outlier mean = 9.65, median = 8.7 and mode = 8.25
Without mean = 8.67, median = 8.65, and mode is 8.25
Mean decreased by .98, median decreased by .05, and mode stayed the same

6. Ex. 3 Finding Range Simply subtract highest and lowest data value
What is the range of contestants on show A?
31 – 19
12 years

7. Ex. 4 Finding Standard Deviation
Find standard deviation of the ages in show B.
Use 𝑠𝑢𝑚 𝑜𝑓 𝑠𝑞𝑢𝑎𝑟𝑒𝑑 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛𝑠 𝑡𝑜𝑡𝑎𝑙 𝑖𝑡𝑒𝑚𝑠
Can make a table if you want, easier to see for some people
Steps
1. find the mean of the data
2. find deviation by taking data value and subtracting the mean found in step 1
3. square each deviation found in step 2
4. add all the squared deviations and then divide by total items
5. take square root of answer from step 4

8. Ex. 4 Continued mean 26 x 25 20 22 27 48 32 19 21 24 x-mean -1 -6 -4 1-7 -5 -2
squared 1 36 16
484 49 25 4
55.8
7.5 years

9. Your Practice Find standard deviation Page 591 number 22
6.7575
2.6

10. Ex. 5 Effects of Data Transformations

11. Ex. 5 Continued
Find the values of the measures shown when each value is increased by Find the values of the measures when values multiplied by 1.2.
Mean = 62, median = 56, mode = 49, range = 46, standard deviation = 15.5
Increased by 14:
Mean = 76, median = 70, mode = 63, range = 46, standard deviation = 15.5
Multiplied by 1.2:
Mean = 74.4, median = 84, mode = 75.6, range = 55.2, standard deviation = 18.6