Chapter 2 Flashcards
Frequency Histograms
Bar graph such that each consecutive must touch (no gaps)
How to create a freq. histogram
- create a table with 3 sections; categories, frequency, relative freq.
- in the categories section put your information ex. 1,2,3,4,5,6
- 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
- then divide your frequency for each # by the total frequency. ex. IF 1 repeats 3 times then the rel. freq.= 3/17=0.18
- create your histogram, frequency on the y-axis, and categories on the x-axis. Remember NO GAPS
How to create a relative freq. histogram
use the info from your relative freq. section and put the relative freq. on the y-axis and categories on x-axis.
NO GAPS
Σ: capital sigma
Sum of
ex. Σx= sum of x
Σx^2=sum of x^2 etc..
Sample mean: x̄ or x bar
Avg.
x̄=Σx/n
Σx=Sum of X
n=sample size
Population Mean M=Mu=μ
μ=Σx/N
Σx=Sum of X
N=pop. size
Sample median:
Middle value in a arranged data set
Sample Mode:
Most frequently occurring value
When to use which measure for the center?
Mean- used for symmetric distribution
median-used for skewed distribution
mode-used for qualitative distribution
Symmetry (bell-shaped) Distribution
Mean ~ Median~ Mode
ex. heights of full-grown men, heights of full-grown women, scores on a standardized exam such as SAT
Left-skewed Distribution
Mean<Median<Mode
ex. ages of people who retired, ages of patients diagnosed with Alzheimer’s disease, and ages of hearing-aid patients.
Right-skewed Distribution
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.
Uniform(Rectangular) Distribution
about the same
ex. # of students at each grade at a public school, rolling a fair die, tossing a fair coin.
Biomodal Distribution
2 modes
Range
Max-Min
Population Variance
σ^2= sigma^2 = Σ(x-mean)^2/n
n=population size
Sample Variance
s^2= Σ(x-mean)^2/n-1
(Σx^2-1/n(Σx)^2) / n-1
n=sample size
Population std dev.
√variance= get rid of the σ^2 by square rooting it √σ^2
Sample std dev.
√variance= get rid of the s^2 by square rooting it √s^2
Variance
Sigma^2 σ^2
Standard Dev.
Sigma, σ
Calculator
Variance=(std. dev.)^2
calc.
vars
5:stats
4: , σx
enter then square answer
Percentile rank
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
First, Second, & Third Quartile
Q2=median in between 25% on each side
Q1=median of the lower set
Q3= median of the upper set
five-number summary
(x max, q1,q2,q3,x min)
Interquartile Range (IQR)
Q3-Q1
Z-score
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.
Empirical Rule
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%
Chebyshev’s Theorem
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.
