Inferences and Conclusions from Data

1. OPEN ENDED Sketch a positively skewed graph. Describe a situation in which you would expect data to be distributed this way.
2. Writing in Math Use the information on page 737 to explain what statistics a teacher should tell the class after a test. Include the mean, median, and mode of the given data set and which measure of central tendency you think best represents the test scores and why. How will the measures of central tendency be affected if Mr. Dent adds 5 points to each score?
3. Writing in Math Use the information on page 762 to explain how surveys are used in marketing. Find the margin of error for those who spend $249 or less if 807 mothers were surveyed. Explain what this margin of error means.

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On Mr. Dent’s most recent Algebra 2 test, his students earned the
following scores.
72 | 70 | 77 769068 81 86 34 94
7184 89 67 19 85 75 668094
:
When his students ask how they did on the test, which measure of
central tendency should Mr. Dent use to describe the scores?
Measures of Central Tendency Data with one variable, such as the test
scores, are called univariate data. Sometimes it is convenient to have
number that describes a set of dat This number is called a measure
central tendency, because it represents the center or middle of the d
The most commonly used measures of central tendency are the mean,
median, and mode.
When deciding which measure of central tendency to use to represent a
set of data, look closely at the data itself.
CONCEPT SUMMARY
Measures of Tendency
When
…
Use
mean the data are spread out, and you want an average of the values
median the data contain outliers
mode the data are tightly clustered around one or two values
KEY CONCEPT
Margin of Sampling Error
If the percent of people in a sample responding in a certain way is p and the size
of the sample is n, then 95% of the time, the percent of the population
responding in that same way will be between p – ME and p + ME, where
P(1-P)
ME = 2V
n
That is, the probability is 0.95 that pu ME will contain the true population results.
EXAMPLE Find a Margin of Error
In a survey of 1000 randomly selected adults, 37% answered “yes” to a
particular question. What is the margin of error?
p(1 – p)
ME = 2 V
Formula for margin of sampling error
11
= 21
= 37% or 0.37, n = 1000
0.37(1 – 0.37)
1000
= 0.030535
Use a calculator
fony
The margin of error is about 3%. This means that there is a 95% chance that
the percent of people in the whole population who would answer “yes” is
between 37 – 3 or 34% and 37 + 3 or 40%.
VICHECK Your Progress
2. In a survey of 625 randomly selected teens, 78% said that they purchase
music. What is the margin of error in this survey?
EXAMPLE
Analyze a Margin of Error
al-World Link
HEALTH In a recent Gallup Poll, 25% of the people surveyed said they
had smoked cigarettes in the past week. The margin of error was 3%.
How many people were surveyed?
p(1 – p)
ME = 2V
Formula for margin of sampling error
rcent of smokers
United States
ation dedined
58.7% in 1985 to
in 2000. New
pies, like the
ne patch, are
ng more people
0.25(1
– 0.25)
0.03 = 2V
ME = 0.03, p = 0.25
11
0.25(0.75)
0.015 =
Divide each side by 2.
3: US Department of
and Human Services
0.000225 =
0.25(0.75)
Square each side.
0.25(0.75)
Multiply by n and divide by 0.000225.
0.000225
1833.33
About 833 people were surveyed.
CHECK Your Progress
3. In a recent survey, 15% of the people surveyed said they had missed a
class or a meeting because they overslept. The margin of error was 4%.
How many people were surveyed?
olige Personal Tutor at algebra2.com