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JV Stats HW & Test # 2

JV Stats HW & Test # 2. OUTLIER FORMULAS BOX PLOTS HISTOGRAMS DESCRIBING A DISTRIBUTION (C.U.S.S.) STANDARD DEVIATION AND VARIANCE. Test #1. Splitting Stems was used in these stemplots. Per 4. Per 2. Period 2 test scores. Find the Median, also called Q 2. 69. Period 2 test scores.

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JV Stats HW & Test # 2

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  1. JV Stats HW & Test # 2 • OUTLIER FORMULAS • BOX PLOTS • HISTOGRAMS • DESCRIBING A DISTRIBUTION (C.U.S.S.) • STANDARD DEVIATION AND VARIANCE

  2. Test #1 Splitting Stems was used in these stemplots Per 4 Per 2

  3. Period 2 test scores Find the Median, also called Q2 69

  4. Period 2 test scores Find Q1 which is median below the Median 59 Find Q3 which is median above the Median 79

  5. Period 2 test scores Give the 5-# summary which is Min, Q1 , Q2 , Q3 , Max 41,59,69,79,97 IQR is the interquartile range IQR = Q3 – Q1 20

  6. Period 2 test scores Checking for Outliers. We have formulas to check high and low numbers TO CHECK for a LOW OUTLIER Q1 – 1.5(IQR) any # smaller is an outlier TO CHECK for a HIGH OUTLIER Q3 + 1.5(IQR) any # larger is an outlier

  7. Create a box plot Outliers Min, Q1 , Q2 , Q3 , Max

  8. Create a box plot of your test scores • Start with a number line below your box plot • Make your increments consistent • Draw the box accurately

  9. Period 4 test scores Find the Median, also called Q2 69

  10. Period 4 test scores Find Q1 which is median below the Median 59 Find Q3 which is median above the Median 83

  11. Period 4 test scores Give the 5-# summary which is Min, Q1 , Q2 , Q3 , Max 41,59,69,83,97 IQR is the interquartile range IQR = Q3 – Q1 24

  12. Period 4 test scores Checking for Outliers. We have formulas to check high and low numbers TO CHECK for a LOW OUTLIER Q1 – 1.5(IQR) any # smaller is an outlier TO CHECK for a HIGH OUTLIER Q3 + 1.5(IQR) any # larger is an outlier

  13. Create a box plot Outliers Min, Q1 , Q2 , Q3 , Max

  14. Create a box plot of your test scores • Start with a number line below your box plot • Make your increments consistent • Draw the box accurately

  15. Back-To-back stemplot

  16. C.U.S.S. • This acronym is used to compare two or more distributions(graphs) C: center……give the mean and median U: unusual features……are there outliers? S: shape……skewed left, skewed right, fairly symmetric….etc S: spread……..give the range….(max – min)

  17. Use the C.U.S.S. acronym to compare two or more distributions

  18. Period 2 has a mean of 69.5 and period 4 has a mean of 69.7. Both classes have a median of 69. There are no outliers for either class. Both distributions are fairly symmetric. Both classes had a min score of 41 and a max score of 97.

  19. Find the 5 # Summary and check for outliers {3,5,2,6,5,1,9,7,4,2,3,23} If you need to, put them in order 1,2,2,3,3,4,5,5,6,7,9,23 5 # Summary {1,2.5,4.5,6.5,23}

  20. Mystery box plot • Here is the 5 # summary of a distribution of a set of 12 numbers {1,7,9,13,22} a) Is it possible that there is no number 9 in the set of numbers? Explain. Yes, since there is an even number of numbers in the set, there is no exact middle number. Example. {1,2,7,8,8,10,10,13,19,22}

  21. Mystery box plot • Here is the 5 # summary of a distribution of a set of 23 numbers {1,7,9,13,22} a) Is it possible that there is no number 9 in the set of numbers? Explain. No, since there is an odd # of numbers in the set, the median must be a number in the set.

  22. Create your set of data • Create a set of data with 20 numbers. • Make sure there are 2 low outliers and 2 high outliers. • Show your outlier formulas to prove that your set meets these requirements. • Create a box plot of your data.

  23. Quartiles • A Box Plot is made up of Q1, Q2, and Q3. • These are called quartiles because they split the box plot into 4 parts. 1 2 3 4 Q1 Q2 Q3 Each of the 4 parts contain 25% of the data

  24. Standard Deviation & Variance • Consider the following set of numbers {1,1,2,2,3,4,5,6,7,9} Find the Mean. Find the distance each # is from your mean, square all those distances and add them up Divide that sum by (n-1)…..this is the Variance Take the square root of the Variance. Now you have the Standard Deviation

  25. What is standard deviation • It is the average distance the set of numbers are from the mean. • It is a measure of spread. • Lower standard deviation means that the numbers in the set are grouped closely around the mean • High standard deviation means that the numbers in the set are widely spread and may possibly have outliers

  26. Find the standard deviation • 1,7,2,10,4,7

  27. Find the standard deviations(Round Means to whole #)

  28. Find the standard deviations(Round Means to whole #)

  29. The Game of Greed

  30. The Game of greed

  31. Find the 5 # Summary {0,16,32,53,73} • Check for Outliers Q1 – 1.5(IQR)…….16 – 1.5(37) = -39.5 Q3 + 1.5(IQR)…….53 + 1.5(37) = 108.5 There are NO OUTLIERS • Draw the Box Plot • Describe the distribution(C.U.S.S.) The mean is 34.3 and the median is 32. There are no outliers. The distribution is fairly symmetric and the range is from 0 to 73.

  32. Histograms • How many times did you go out to eat over the weekend? • Before we create our histogram we need to make a frequency table.

  33. Create the histogram

  34. Calculate the mean of a histogram

  35. Describe the distribution (c.u.s.s.)

  36. Different types of histograms Bars are centered on the numbers Bars are for a given range Your data will help you decide which type is better

  37. Outfiers affect Range, Mean, Variance, and Standard Deviation. An outlier causes all these to increase or decrease Outliers do not affect the median and IQR.

  38. Coin in a cup activity Given 3 minutes for your strong hand and 3 minutes for your weak hand. How many quarters can you bounce in a cup? Is your strong hand better than your weak? To reduce bias student flipped a coin to determine whether they would use their strong or weak hands for the first 3 minutes. This is done because students may learn how to bounce their coins and get better the second time around.

  39. Coin in a cup activity

  40. Coin in a cup activity PER 2

  41. Coin in the cup activity PER 2

  42. Compare the Strong and Weak C.U.S.S. The median of the strong is 3.5 and the median of the weak is 2. The mean of the strong is 4.1 and the mean of the weak is 3.5. There are no outliers. Both distributions are skewed to the right. The strong ranges from 0 to 12 and the weak ranges from 0 to 10.

  43. Find the Standard Deviation 1,4,6,3,7,8,1,8,7

  44. Check for outliers 1,25,23,38,45,45,48,53,67,72,76

  45. Check for outliers 1,25,23,38,45,45,48,53,67,72,76

  46. Create a boxplot 1,25,23,38,45,45,48,53,67,72,76

  47. Find the mean and median of a histogram

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