Chapter 2

Question 1

Frequency Histograms

Answer 1

Bar graph such that each consecutive must touch (no gaps)

Question 2

How to create a freq. histogram

Answer 2

1. create a table with 3 sections; categories, frequency, relative freq.
2. in the categories section put your information ex. 1,2,3,4,5,6
3. in the freq. section put how many times that number repeats then add the frequency and that will give you the number you need to divide by in order to get rel. freq. ex. frequency= 17
4. then divide your frequency for each # by the total frequency. ex. IF 1 repeats 3 times then the rel. freq.= 3/17=0.18
5. create your histogram, frequency on the y-axis, and categories on the x-axis. Remember NO GAPS

Question 3

How to create a relative freq. histogram

Answer 3

use the info from your relative freq. section and put the relative freq. on the y-axis and categories on x-axis.
NO GAPS

Question 4

Σ: capital sigma

Answer 4

Sum of
ex. Σx= sum of x
Σx^2=sum of x^2 etc..

Question 5

Sample mean: x̄ or x bar
Avg.

Answer 5

x̄=Σx/n
Σx=Sum of X
n=sample size

Question 6

Population Mean M=Mu=μ

Answer 6

μ=Σx/N
Σx=Sum of X
N=pop. size

Question 7

Sample median:

Answer 7

Middle value in a arranged data set

Question 8

Sample Mode:

Answer 8

Most frequently occurring value

Question 9

When to use which measure for the center?

Answer 9

Mean- used for symmetric distribution
median-used for skewed distribution
mode-used for qualitative distribution

Question 10

Symmetry (bell-shaped) Distribution

Answer 10

Mean ~ Median~ Mode
ex. heights of full-grown men, heights of full-grown women, scores on a standardized exam such as SAT

Question 11

Left-skewed Distribution

Answer 11

Mean<Median<Mode
ex. ages of people who retired, ages of patients diagnosed with Alzheimer’s disease, and ages of hearing-aid patients.

Question 12

Right-skewed Distribution

Answer 12

Mode<Median<Mean
ex. prices of homes in the US, prices of cars, number of children in a family, annual income in a household in a country.

Question 13

Uniform(Rectangular) Distribution

Answer 13

about the same
ex. # of students at each grade at a public school, rolling a fair die, tossing a fair coin.

Question 14

Biomodal Distribution

Answer 14

2 modes

Question 15

Range

Answer 15

Max-Min

Question 16

Population Variance

Answer 16

σ^2= sigma^2 = Σ(x-mean)^2/n
n=population size

Question 17

Sample Variance

Answer 17

s^2= Σ(x-mean)^2/n-1
(Σx^2-1/n(Σx)^2) / n-1
n=sample size

Question 18

Population std dev.

Answer 18

√variance= get rid of the σ^2 by square rooting it √σ^2

Question 19

Sample std dev.

Answer 19

√variance= get rid of the s^2 by square rooting it √s^2

Question 20

Variance

Answer 20

Sigma^2 σ^2

Question 21

Standard Dev.

Answer 21

Sigma, σ

Question 22

Calculator

Answer 22

Variance=(std. dev.)^2
calc.
vars
5:stats
4: , σx
enter then square answer

Question 23

Percentile rank

Answer 23

data points at or below the point of interest/ total # of data points
ex.
percentile rank of 4= # data values less than or = to 4 divided by total data size
0,0,1,2,3,3,5,7,7,7,10
6/11=0.55 55th percentile rank

Question 24

First, Second, & Third Quartile

Answer 24

Q2=median in between 25% on each side
Q1=median of the lower set
Q3= median of the upper set

Question 25

five-number summary

Answer 25

(x max, q1,q2,q3,x min)

Question 26

Interquartile Range (IQR)

Answer 26

Q3-Q1

Question 27

Z-score

Answer 27

Reliable to be used for bell-shaped or symmetric distribution
z=( data-x -mean)/ std. dev. of either sample or pop.
negative z score= below avg.
positive z score = above avg.
zero=exactly @ the avg.

Question 28

Empirical Rule

Answer 28

ONLY FOR BELL-SHAPED DISTRIBUTION
-mean goes in the middle
approx. 68% of data lie within ONE std. dev. of the mean
34%/34%

approx. 95% of data lie within TWO std. dev. of the mean
13.5%/13.5%

Approx. 99.7% of data lie within THREE std. dev. of the mean
2.35%/2.35%
outliers= 0.15%/0.15%

Question 29

Chebyshev’s Theorem

Answer 29

USED FOR DISTRIBUTION OF DATA THAT’S UNKNOWN OR SKEWED

at least 3/4 of data lie within 2 std. dev. of the mean
mean +- 2 std. dev.
at least 8/9 of data lie within 3 std. dev. of the mean
88.9% mean+- 3 std. dev.
at least 1-(1/k^2) of the data falls within K std. devs.