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Advanced Math Topics

Advanced Math Topics. Review of Chapters 2 and 3. average. 1. $2375-. 2539. 2457. I. 1. 1/50. $165. 2. $2540-. 2704. 2622. 0. 0. 3. $2705-. 2869. 2787. 0. 0. These are the main columns!!. 4. $2870-. 3034. 2952. 0. 0. $3035-. 3199. 3117. 0. 0. 5. 6.

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Advanced Math Topics

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  1. Advanced Math Topics Review of Chapters 2 and 3

  2. average 1 $2375- 2539 2457 I 1 1/50 $165 2 $2540- 2704 2622 0 0 3 $2705- 2869 2787 0 0 These are the main columns!! 4 $2870- 3034 2952 0 0 $3035- 3199 3117 0 0 5 6 $3200- 3364 3282 IIIII IIIII III 13 13/50 7 $3365- 3529 3447 IIIII III 8 8/50 $3530- 3694 3612 IIIII IIIII 10 10/50 8 9 $3695- 3859 3777 IIIII IIII 9 9/50 10 $3860- 4024 3942 IIIII IIII 9 9/50 Class Average total frequency Helps us talk about classes easier! Class Average (midpoint) Lower limit-upper limit

  3. Index number: a ratio used to show % changes over time They allow us to compare prices, products, sales figures, and more for a given period of time against an earlier period of time. The earlier period of time is called the base period. given year’s value Index number = X 100 base year’s value

  4. The number of yearly visitors to the SRVUSD website over a six year period is as follows: Using 2001 as a base year, calculate the index number for each year and evaluate using % increase or % decrease. Year Visitors Index Number % Change from 2001 418,355 X 100 = 100 0% Change from 2001 2001 418,355 418,355 117.46-100 = 17.46% Increase in hits from 2001 491,398 X 100 = 117.46 2002 491,398 418,355 98.41-100 = 1.59% Decrease in hits from 2001 411,688 2003 411,688 X 100 = 98.41 418,355 116.86-100 = 16.86% Increase in hits from 2001 488,894 2004 488,894 X 100 = 116.86 418,355 120.33-100 = 20.33% Increase in hits from 2001 503,391 2005 503,391 X 100 = 120.33 418,355 120.79-100 = 20.79% Increase in hits from 2001 505,320 2006 505,320 X 100 = 120.79 418,355

  5. G.E. sampled 60 light bulbs for their length of life. Find the a) sample mean, • b) median, and c) mode of the grouped data. Class mark • class frequency Σ xf a) Sample Mean of Grouped Data = x = Σ f Total frequency Class Mark(x) x • f Σ xf 4740 79 = = Σ f 60 44.5 222.5 54.5 381.5 b) Median = class mark of the middle frequency 64.5 516.0 The frequency is 60 so the 30th and 31st numbers will tell us the median. 74.5 670.5 = 84.5 84.5 1014 94.5 850.5 c) Mode is in the interval. 80-89 104.5 627.0 114.5 458.0 4740 60

  6. Chebyshev’s Theorem In any population or sample… Let k be any number equal to or greater than 1, Then the proportion of any distribution that lies Within k standard deviations of the mean is at least… 1 - 1 k2

  7. What does this theorem mean? Computing some values of k… What does this look like? 1 Remember k = the standard deviation = s 1 - k (Std. deviations) k2 1 At least 75% of the data will lie in this interval. 1 - = 0 = 0% 1 12 1 x + 2s x – 2s x 1 - = 3/4 = .75 = 75% 2 22 At least 88.89% of the data will lie in this interval. 1 1 - = 8/9 = .8889 = 88.89% 3 32 x + 3s x – 3s x

  8. The number of terms equal to x, including x. The number of terms below x. B + ½ E • 100 Percentile rank of X = N The number of total terms, including x.

  9. The test score of Ron (80) and his class is shown in the data below. Find his percentile • rank. Ron’s Class 64, 67, 73, 73, 73, 74, 77, 77, 78, 78, 79, 80, 80, 82, 91, 94, 100 ½ (2) 11 + Ron’s percentile rank = • 100 = 70.59 17 Ron’s percentile rank is 70.59.

  10. New York rated its top 5 pizza companies and San Francisco did the same, but they used different scales. A high score shows that people enjoyed the pizza. The results are: X – X s z-score of x = Which brand has the least taste appeal? At first glance, David’s seems to be the lowest. But since there were different scales and other relative scores to consider, we must find the z-score. David’s 1 – 15 10.32 z-score = = -1.36 Domino’s 25 – 45 16.96 z-score = = -1.18 The worst rated pizzeria was David’s because it has the lowest z-score. x = 15 x = 45 s = 10.32 s = 16.96

  11. HW • P. 94 #5, 13, 14 • P. 168 # 1,2, 4(mean only), 11, 14 Makeups this Thursday P. 2 Jake Whitney Ch. 10 Natalie Schutzman Ch. 10 Matt Finegold Ch. 10 P. 3 Erin Hathaway Ch. 3 Quiz, Ch. 8 Test Jenna Narez Ch. 5 Test Dan Smithwick Ch. 10 Test Kimmy Pong Ch. 10 Brad Wilson Ch. 10 Ryan Fitzgerald Ch. 10 P. 4 Miles Spafford Nicole Tarantino Hannah Forman David Fehlman Steve Roberts and Miles Spafford How to figure out your grade before finals…

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