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Statistics

Statistics. Mean, Median, Mode, Range, Standard Deviation Histograms, Stem & Leaf, Box & Whiskers. Data. 235 218 210 205 235 261 188 250 175 220 217 229 240 225. Find the Mean. 235 218 210 205 235 261 188 250 175 220 217 229 240 225 3108. Add ‘em up Divide by

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Statistics

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  1. Statistics Mean, Median, Mode, Range, Standard Deviation Histograms, Stem & Leaf, Box & Whiskers

  2. Data 235 218 210 205 235 261 188 250 175 220 217 229 240 225

  3. Find the Mean 235 218 210 205 235 261 188 250 175 220 217 229 240 225 3108 • Add ‘em up • Divide by How many 3108 / 14 = 222

  4. Median • Must be in order – Middle • If there are 2 middles – average them • 235 175 • 218 188 • 210 205 • 205 210 • 235 217 • 261 218 • 188 220 • 250 225 • 175 229 • 220 235 • 217 235 • 229 240 • 240 250 • 225 261

  5. Mode • Sounds like….Most • 235 • 218 • 210 • 205 • 235 • 261 • 188 • 250 • 175 • 220 • 217 • 229 • 240 • 225

  6. Range • Not a range like 175-261 • Subtract: 261-175 = 86 • 235 • 218 • 210 • 205 • 235 • 261 • 188 • 250 • 175 • 220 • 217 • 229 • 240 • 225

  7. Subtract the mean from each score 235-222 = 13 218-222 = -4 210-222 = -12 205-222 = -17 235-222 = 13 261-222 = 39 188-222 = -4 250-222 = 28 175-222 = -47 220-222 = -2 217-222 = -5 229-222 = 7 240-222 = 18 225-222 = 3

  8. Square them & add them up 235-222 = 13……….. 169 218-222 = -4………... 16 210-222 = -12………. 144 205-222 = -17………. 289 235-222 = 13……….. 169 261-222 = 39……….. 1521 188-222 = -4………… 16 250-222 = 28……….. 784 175-222 = -47………. 2209 220-222 = -2………… 4 217-222 = -5………… 25 229-222 = 7…………. 49 240-222 = 18………... 324 225-222 = 3…………. 9 Total = 5728

  9. Divide by n & square root • 5728/ 14 = 409.143 • Square root of 409.143= 20.227 • SD = 20.227 Can approx. with 20 • So what???

  10. Histogram • Group data so each score is not listed separately • Each should be the same size • Don’t leave out any groups - just show a 0

  11. Stem & Leaf • List only the first digit in the left hand column • List the last digit in the right hand column, list repeats 17 18 20 21 22 5 8 5 0, 7, 8 0, 5, 9

  12. Box & Whiskers 235 175 218 188 210 205 205 210 235 217 261 218 188 220 250 225 175 229 220 235 217 235 229 240 240 250 225 261 • Find the median • Find the high • Find the low • Find the median • of each half

  13. Normal Distribution

  14. My Normal Curve… 162 182 202 222 242 262 282 In theory… 68% of weights will be between 202 & 242. In reality 10 out of 14 were. That is 71.4% - pretty close. In theory…95% of weights will be between 182 & 262. In reality 13 out of 14 are. That is 93.9%

  15. Using the Normal Curve & Predictions… • Z-scores • (Score-average) / SD • Example: What percent of weights should be below 235 on my team? (235-222) / 20 = .75 Look it up on chart

  16. That means almost 27% should be between the .75 and the middle (222-235 lbs) And 50% are below the 222 so the total below 235 is 77%

  17. Try another…What % should be above 225lbs (225-222) / 20 = .15 Look it up. Approx. 6% 6% is between 225 & 222 so with 50% on that side total, it leaves 44% above 225.

  18. What about between 190 & 200?

  19. Correlation • Positive: as one increases so does the other - Height & Weight • Negative: as one increases the other decreases - Age of car & value (exceptions) • None: no pattern - Age & Shoe Size

  20. Scatter Plots

  21. Line of Best Fit (261, 82) (210, 75) y = mx + b 75 = (7/51)(210) + b 75 = 1470/51 + b 1470/51 ~ 29 75 = 29 + b almost 46 = b y = (7/51)x + 46 almost Slope= (82-75)/261-210) m= 7/51

  22. Predictions • Y=29x + 46 would give me a way to predict the height of a player if I know their weight or vice versa. • Example: If a player weighs 233 pounds, that would be x so plug it into the equation. • Y=(7/51) (233)+ 46 • Y = 77.98 inches…. About 6’ 6” Check it on the scatter plot. Does it look about right?

  23. Correlation Coefficient • How good is my prediction? • 235 x 77 = 18095 • 218 x 75 = 16350 • 210 x 75 = 15750 • 205 x 73 = 14965 • 235 x 80 = 18800 • 261 x 82 = 21402 • 188 x 70 = 13160 • 250 x 80 = 20000 • 175 x 72 = 12600 • 220 x 75 = 16500 • 217 x 73 = 15841 • 229 x 76 = 17404 • 240 x 80 = 19200 • x 79 = 17775 • Total = 237842 • Multiply all the pairs together • Add them up • Divide by n • Subtract the product of the means • Divide by the product of the standard • deviations 237842 - (222)(76.2) 14 _________________ = .929 ~ 93% (22.9) (3.4) Keep in mind that we rounded in a couple of places so there is round-off error.

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