Download Chapter 2 Review

AP Statistics
Chapter 2 Review
Do you know …
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Formulas for mean, variance, standard deviation, grouped standard deviation, and z-scores for both
sample and population
Empirical Rule percentages
Outline of a bell-shaped distribution with data, percentages, z-scores
Chebychev’s Theorem
Five number summary
how to draw a box-and-whisker plot
how to identify outliers of a data set
1.) FORMULAS:
Sample
mean
variance
standard deviation
grouped standard deviation
z-score
2.) A sample of inch measures is shown. 6, 5, 4, 1 inches
Calculate the standard deviation by hand. (Show substitution into formula or chart)
3.) A population of in measures is shown. 6, 5, 4, 1 inches
Calculate the standard deviation by hand. (Show substitution into formula or chart)
Population
4.) Estimate the sample mean and sample standard deviation from this sample of grouped data of college
students’ ages.
class
17 – 21
22 – 26
27 – 31
frequency
30
15
5
5.) Given that the mean of the data set is 66.8 inches and the standard deviation is 1.92 inches, use Chebychev’s
Theorem to find the following.
What percentage of the data must lie within 3 inches of the mean?
6.) Suppose we then learn the height data is bell shaped. The mean is still 66.8 inches and the standard
deviation is 1.92 inches. Use the _______________________Rule to find the following.
a.) draw the data showing the bell shape and identifying the mean and the first three standard
deviations.
b.) on your drawing, also identify the percent of data that lies within each region.
c.) Find the interval of inches that lie in the middle 95% of inch heights.
d.) Find the inch heights that fall in the extreme 5% of inch heights
e.) Label the bell curve with the z-score intervals
f.) Calculate the z-score for 70 inches.
7.) Find the five number summary of the following data cm lengths
34, 35, 33, 26, 9, 28, 39, 27, 34
Find the IQR
Are there outliers? If so, which?
Draw a box-and-whisker plot
̅ = 67, s = 2.8, n = 150. Between which two heights do we
8.) A set of data measuring heights in inches has 𝒙
expect at least 96% of heights to lie?
9.) A sample of weights (in pounds) of 4 NFL players is found. The weights are 270, 257, 255, 266.
Range:
Mean:
Variance:
Standard Deviation:
10.) Here is a frequency distribution of free throws made for the Butler Basketball team.
free throws made
51 – 75
76 – 100
101 – 125
f
8
12
5
Sample Size:
Estimate the sample mean from the grouped data:
Find the sample standard deviation from the data:
11.) In a sample of 1000 SAT scores the sample was found to be approximately bell shaped (use Empirical Rule)
with mean 1380 and standard deviation 90.
Draw a sketch of the distribution, labeling it with the SAT scores, the percent of data within each section.
Approximately how many students scored between 1290 and 1470?
If a school only accepts students with SAT scores of 1560 or above then, based only on SAT scores,
about what percentage of applicants would you expect them to accept?
Approximately what percentage of scores will fall between 1470 and 1560?
When Steve took the SAT he scored in the bottom 16% of all students. What was his maximum possible
score?
12.) In a statistical experiment we collect the GPA of all students in an AP course at Butler SHS. After collecting
the data we determine that the mean is 3.5 and the standard deviation is 0.13. We do not know if the data is
bell shaped.
a.) If GPAs between 3.2 and 3.8 are given an A on a report card, at lease what percent of students in
AP courses must be getting As?
b.) Between which two scores do we know that 84% of the data lies?
c.) Suppose later we find out the data is bell shaped and there are 200 students in AP classes. If honor
roll is given to any students with GPA above 3.24, about how many students in AP classes will make honor roll.