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Advanced Math Topics Review of Chapters 2 and 3.

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Presentation on theme: "Advanced Math Topics Review of Chapters 2 and 3."— Presentation transcript:

1 Advanced Math Topics Review of Chapters 2 and 3

2 These are the main columns!! 1 2 3 4 5 6 7 8 9 10 Class # Class Mark
Class(Interval) Car Offers Class Mark Tally Frequency Relative Frequency average 1 $2375- 2539 2457 I 1 1/50 $165 2 $2540- 2704 2622 3 $2705- 2869 2787 These are the main columns!! 4 $2870- 3034 2952 5 $3035- 3199 3117 6 $3200- 3364 3282 IIIII IIIII III 13 13/50 7 $3365- 3529 3447 IIIII III 8 8/50 8 $3530- 3694 3612 IIIII IIIII 10 10/50 9 $3695- 3859 3777 IIIII IIII 9 9/50 10 $3860- 4024 3942 IIIII IIII 9 9/50 Helps us talk about classes easier! Class Average total frequency 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 = 17.46% Increase in hits from 2001 491,398 2002 491,398 X 100 = 117.46 418,355 = 1.59% Decrease in hits from 2001 411,688 2003 411,688 X 100 = 98.41 418,355 = 16.86% Increase in hits from 2001 488,894 2004 488,894 X 100 = 116.86 418,355 = 20.33% Increase in hits from 2001 2005 503,391 503,391 X 100 = 120.33 418,355 = 20.79% Increase in hits from 2001 2006 505,320 505,320 X 100 = 120.79 418,355

5 f Σ xf a) Sample Mean of Grouped Data = x = Σ f Σ xf 4740 79 Σ f 60
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 Bulb Life (hrs.) f 40-49 5 50-59 7 60-69 8 70-79 9 80-89 12 90-99 6 4 Class Mark(x) x • f Σ xf 4740 = = 79 44.5 222.5 Σ f 60 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 1014 84.5 94.5 850.5 c) Mode is in the interval. 80-89 104.5 627.0 114.5 458.0 60 4740

6 1 - Chebyshev’s Theorem 1 k2 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 k (Std. deviations) 1 - k2 1 At least 75% of the data will lie in this interval. 1 - = 0 = 0% 1 12 1 1 - x – 2s x x + 2s = 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 x + 3s

8 B + ½ E • 100 N Percentile rank of X = 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 Ron’s percentile rank = • 100 = 70.59 17
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 11 + ½ (2) Ron’s percentile rank = • 100 = 70.59 17 Ron’s percentile rank is

10 X – X s z-score of x = 1 – 15 z-score = 10.32 = -1.36 25 – 45
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 Brand NY Rating David’s 1 Mama Mia’s 10 Papa John’s 15 Round Table 21 Pizza Time 28 Brand SF Rating Domino’s 25 Pizza Hut 35 Zachary’s 45 Mt. Mike’s 50 Pavlo’s 70 z-score = 10.32 = Domino’s 25 – 45 z-score = 16.96 = 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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