Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
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 • • • • • • • 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 • • • • • • • 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