Mean (?, quantitative without outliers)
sum of all data points / number of data points
NOTE: round answer to one more decimal place than the highest number of decimal places contained in the data.
Deviation (Statistics)
Measure of difference between the observed value of a variable and some other value, often that variable's mean.
Weighted Mean x?
x? = ?(each value multiplied by its respective weight) / ? (each weight)
Ex:
Test weight/score: 70% / 92
Homework weight/score: 20% / 100
Attendance weight: 10% / 95
x? = [92(.70)+100(.20)+95(.10)] / .70+.20+.10
Median (quantitative WITH outliers)
Data value in the middle of an ordered array. The same number of data values is on either side of the median value.
NOTE: If the number of data values is even, the median is the mean of the middle two numbers.
Mode (ordinal, nominal [qualitative data])
Data value which occurs the most number of times.
No data occurs more than once = no mode
Each value occur equally = no mode
One value occur the most = unimodal
Two values occur the most = bimodal
Three values occur the most = multimodal
Range
Difference between the largest and the smallest data value.
Deviation
Difference in a data value and another measure, such as mean. Deviation from mean = xi - x? (xi is a data value)
The sum of the deviations from the man for any data set is always equal to zero:
?(xi-x?)=0
Variance (population)
?^2 = ?(xi-?)^2 / N
xi is the ith data value in the data set
? is the population mean
N is the size of the population
Variance (sample)
s^2 = ?(xi-x?)^2 / n-1
xi is the ith data value in the data set
x? is the sample mean
n is the size of the sample
Variance Rounding Rule
Round variances to one more decimal place than the highest number of decimal places contained in the data. If you are not given actual data, but have a mean, round to the same number of decimal places as the mean.
Standard Deviation
Square root of the variance.
s = ?s^2 (sample)
? = ??^2 (population)
Standard Deviation Rounding Rule
Round standard deviation to one more decimal place than the highest number of decimal places contained in the data. If you are not given actual data, but have a mean, round to the same number of decimal places as the mean.
Coefficient of Variation (CV)
Ration of the standard deviation to the mean as a percentage.
CV = s/x? (100%) (sample)
CV = s/? (100%)
Standard Deviation (grouped data)
?n[?(f?x^2)]-[?(f?x)]^2 / n(n-1)
n = sample size
f = frequency
x = midpoint
Empirical Rule
For the normal distribution (bell-shaped distribution), approximately 68% of the measurements are within one standard deviation of the mean, approximately 95% of the measurements are within two standard deviations of the mean, and approximately 99.7% of t
Empirical Rule Example
The distribution of heights of girls is bell shaped. mean=106.68cm, standard deviation = 3.81cm.
1) What % girls between 92.25cm and 118.11cm?
Answer:
92.25 - mean(106.68) = 11.43.
11.43 / standard deviation(3.81) = -3
118.11 - mean(106.68) = 11.43.
Accor
Chebyshev's Theorem
The proportion of data that lies within K standard deviations of the mean is at least 1 - 1/K^2, for K>1. When K=2 and K=3, Chebyshev's Theorem says:
K=2: At least 1-1/2^2 = 3/4 = 75% of the data lies within two standard deviations of the mean
K=3: At lea
Chebyshev's Theorem Example
http://i.imgur.com/X6tvzBR.png
Percentile (find data value for Pth percentile)
http://i.imgur.com/sWOwJPt.png
Percentile (find the Pth percentile for a value)
http://i.imgur.com/t8cd0tP.png
Box Plot
http://i.imgur.com/wj2m5lv.png
What a Box Plot can tell you
http://i.imgur.com/sqxVgYP.png
Interquartile Range (IQR)
Range of the middle 50% of the data, given by:
IQR = Q3 - Q1
Standard Score (z-score)
http://i.imgur.com/3YL7zr6.png