What We Will Learn Compare mean median and mode Find range and standard deviation Identify effects of transformations on data Needed Vocab Measure of center mean median and mode Mean sum of the data divided by total number of data values aka average ID: 735949
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Slide1
11.1 Measures of Center and VariationSlide2
What We Will Learn
Compare mean, median, and mode
Find range and standard deviation
Identify effects of transformations on dataSlide3
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 setSlide4
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 2Mode = 8.25Median - 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
8.25
9.10
9.25Slide5
Ex. 2 Removing an Outlier
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
Hourly
Wages
16.50
8.25
8.75
8.45
8.65
8.259.109.25
Mean decreased by .98, median decreased by .05, and mode stayed the sameSlide6
Ex. 3 Finding Range
Simply subtract highest and lowest data value
What is the range of contestants on show A?
31 – 19
12 yearsSlide7
Ex. 4 Finding Standard Deviation
Find standard deviation of the ages in show B.
Use
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 4Slide8
Ex. 4 Continued
55.8
7.5 years
x
25
20
22
27
48
32
19
27
25
22
21
24
mean
26
26
26
26
26
26
26
2626262626
x-mean-1-6-41226-71-1-4-5-2
squared
1
36
16
1
484
36
49
1
1
16
25
4Slide9
Your Practice
Find standard deviation
Page 591 number 22
6.7575
2.6
Slide10
Ex. 5 Effects of Data TransformationsSlide11
Ex. 5 Continued
Find the values of the measures shown when each value is increased by 14. 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