How can we help?

You can also find more resources in our Help Center.

48 terms

Statistics Test 1

STUDY
PLAY
Types of Charts or Graphs
...
Frequency Polygon
X axis = score, Y axis = frequency, type of line graph that shows frequency distributions. Uses mid-point to plot connect back to axis.
Bar Graph
A graph that uses horizontal or vertical bars to display countable data
Time Series
construct with time (Jan, Feb, March) on x axis
and values oi y axis
Frequency Histogram
Construct using rectangles that are the same width and touch each other. Heights of the bars represent observed frequencies. If large amounts of data using classes, use lower class limits on x axis.
Different types of histograms
Same as frequency histogram but uses specific frequency values. Ex. Relative Frequency, Cumulative Frequency, Cumulative Relative Frequency.
Pie Chart
construct using relative frequency and multiply by 360 to get angle on pie chart
Ogive
Point chart based off of cumulative frequency. Plots upper limit of each class. Does not connect to axis. * Relative ogive uses relative frequency values
Symbols
...
summation
μ
population mean
add all values of population and divide by number of values
xbar
Sample Mean
add all values of sample and divide by number of values
...................∑xi fi
xbar=..........-------
....................∑ fi
N
Size of population
n
Size of sample
i
values of μ (population) or x-bar (sample) individual values
M
median value in middle when arranged in ascending order
If there are odd number of values there will be two middle values. Add the two middle values and divide by 2.
R
range
Largest number minus smallest number to get range
not resistant
...2
s
Sample Variance of raw data not in classes, needs 4 columns

s2= ∑(x -xbar) 2(squared)
..................----------------
......................... n-1
same formula expanded
s2= (X1-xbar)2 +(X2-xbar)2+(X3-xbar)2
........-------------------------------------------
......................... n-1
s
Sample standard variation
not resistant
...2
s
Sample Variance of data in classes, needs 8 columns
...2
σ
Population Variance
Population Variance of raw data not in classes, needs 4 columns

σ 2= ∑(x -μ) 2(squared)
___________________
.................N

σ 2= (X1-μ)2 +(X2-μ)2+(X3-μ)2
__________________________
................N
not resistant
...2
s
..., population standard deviation
σ = √ σ2
not resistant
...2
σ
Population Variance of data in classes, needs 8 columns
f
frequency or fences
IQR
Inter Quartile Range - the middle 50% , resistant
use this if data is skewed left or right better measure of dispersion
Q2=
Median
z
z score
x- mean(either xbar or μ)
----------------------------------
Standard deviation (either σ or s)
xbar w
weighted mean
.................∑wi x
XBAR w= ---------
...................∑w
Pk
kth percentile are < or equal to value data
ex. P1=1%, P2=2%.....P99=99%
Definitions
...
Mean average
The sum of the numbers in a data set divided by the number of items in the data set.
Median
Middle number in a set of numbers that are listed in order
Mode
the most frequent value occurring in a data set
* The mode is the only method used with non value (ex color) for central tenancy
When a bell shaped chart is skewed Left
mean< median
When a bell shaped chart is skewed Right
mean>median
When a bell shaped chart is symmetric
mean=median
Cumulative Frequency
a running total of frequencies
ex. First value is constant
2nd value is sum of 1st and 2nd value
3rd value is sum of 1st, 2nd and 3rd value.
Cumulative Relative Frequency
a running total of relative frequencies
ex. First value is constant
2nd value is sum of 1st and 2nd value
3rd value is sum of 1st, 2nd and 3rd value.
Frequency
How many times something occurs, the number of observations in a given statistical category,
Relative Frequency
Individual frequency divided by the sum of all frequencies.
The ratio of the number of observations in a statistical category to the total number of observations.
Deviation
deviation = Xi- μ or Xi- xbar
summations of all deviations should equal 0
Discrete
You can count the values
Continuous
Infinite number of possible values NOT countable
Empirical Rule
Bell shaped distribution
~68% of data will be in 1st deviation (μ +/- 1σ)
~95% of data will be in 2nd deviation (μ +/- 2σ)
~99.7% of data will be in 3rd deviation (μ +/- 3σ)
fences
cutoff point for determining outliers
Lower Fence
Q1 - 1.5(IQR)
Upper Fence
Q3 + 1.5(IQR)
outliers
extreme observations