Transcript Chapter 3 Lesson 3

CHAPTER 3 LESSON 3
TRANSLATIONS OF DATA
VOCABULARY
• Translation- a transformation that maps each xi to
xi+h, where h is a constant
• Invariant- Unchanged by a particular
transformation
SUMMARY STATISTICS
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•
•
•
•
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•
Mean
Median
Mode
Range
Inter-Quartile Range (IQR)
Variance
Standard Deviation
QUESTIONS
• What happens to the summary statistics when I take
all of the data points and add the same number to
all of them?
• What happens if I subtract the same number to all
of the data points?
HOW TO FIND MEAN MEDIAN AND
MODE
• Mean?
• Median?
• Mode?
MEAN MEDIAN AND MODE
1
1
• Mean?
• Median?
• Mode?
2
4
6
7
7
7
8
9
9
11
NOW WHAT HAPPENS IF I ADD 3 TO
ALL THE NUMBERS?
4
4
5
• Mean?
• Median?
• Mode?
7
9
10
10
10
11
12
12
14
HOW DID THE SUMMARY STATISTICS
CHANGE?
• Mean?
• Median?
• Mode?
WHAT WOULD THE MEASURES BE IF I SUBTRACTED 2
FROM ALL THE ORIGINAL DATA VALUES?
• Mean?
• Median?
• Mode?
EFFECTS OF TRANSLATIONS
• Adding/subtracting some number (h) to each
number in a data set will add/subtract that same
number (h) to each of the mean, median and
mode.
HOW TO FIND RANGE, IQR, VARIANCE
AND STANDARD DEVIATION
• Range?
• IQR?
• Variance?
• Standard Deviation?
RANGE, IQR, VARIANCE, STANDARD
DEVIATION
1
1
2
4
6
• Range?
• IQR?
• Variance?
• Standard Deviation?
7
7
7
8
9
9
11
WHAT WOULD HAPPEN IF I ADD 3 TO
ALL THE VALUES?
4
4
5
7
9
10
• Range?
• IQR?
• Variance?
• Standard Deviation?
10
10
11
12
12
14
HOW DID THE SUMMARY STATISTICS
CHANGE?
• Range?
• IQR?
• Variance?
• Standard Deviation?
WHAT WOULD THE SUMMARY STATISTIC VALUES BE
IF I SUBTRACTED 2 FROM ALL THE ORIGINAL
VALUES?
• Range?
• IQR?
• Variance?
• Standard Deviation?
EFFECTS OF TRANSLATIONS
• Adding/subtracting some number (h) to each
number in a data set will not change the range,
interquartile range (IQR), variance, or standard
deviation of the data
• These statistics are called invariant
EXAMPLE
• If I added 10 to every number in the data set what would my
new values be?
Original
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•
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Mean – 22
Mode – 25
Range – 20
Median – 24
IQR – 10
Variance – 16
Standard Deviation – 4
After adding 10
→
→
→
→
→
→
→
MeanModeRangeMedianIQRVarianceStandard Deviation-
TRANSFORMATION
• Identify the transformation below
Original Scores
3
4
6
9
11
Frequency
2
2
1
4
2
Transformed
Scores
11
12
14
17
19
Frequency
2
2
1
4
2
TRANSFORMATION
Original Scores
3
4
6
9
11
Frequency
2
2
1
4
2
Transformed
Scores
11
12
14
17
19
Frequency
2
2
1
4
2
• Range Original?
Range Transformed?
• Mode Original?
Mode Transformed?
• Mean Original?
Mean Transformed?
• Median Original?
Median Transformed?
SUPPOSE….
• X1=1
X2= -2
X 3= 4
X4= 0.5
X5= 3.5
5
∑ (xi + 5) = (6+3+9+5.5+8.5) = 32
i=1
5
∑ Xi + 5 = (1 + (-2) + 4 + 0.5 + 3.5) + 5 = 12
i=1
• Notice a difference?
EXAMPLE
• X1= 11
4
∑ (Xi + 7) =
i=1
4
∑ Xi + 7 =
i=1
X2= 9
X3=4
X4= 6
EVALUATE EXPRESSIONS FOR
F:X→X ± K
• When given these instructions, you will be given a
number to start out with, f(5) for example.
• To get the transformation, take the starting number
and apply the addition or subtraction given in the
instructions
• For example F:X →X + 2
• F(5) = 5 + 2 = 7
• F(5)=7
EVALUATE EXPRESSIONS FOR
F:X→ X - 3
• F(1.5)
• F(-3)
• F(b)
EVALUATE EXPRESSIONS FOR
F:X→X + 4
• F(2)
• F(5)
• F(a)
HOMEWORK
• Worksheet 3-3