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…