Week 1-Topic 2 Central Tendency And Measure Of Dispersion Flashcards
Measures of central tendency
Mean median mode
Measures of dispersion
Range
Variance and standard deviation
Weighted population mean
Frequency x Value
/
N
3 shapes of data
Symmetrical
Positive skew
Negative skew
Symmetrical distribution
Mean=mode=median
Positive skew vs negative skew
Mean>median>mode
Mode>median>mean
(Visually, mean is always halfway)
What does Geometric mean do and formula
Finds average change in rates overtime
N to the root of the value
Geometric mean to find average percentage overtime. (WHEN ONLY HAVE INITIAL AND FINAL VALUES)
N to the root (VALUE AT END/VALUE AT START) -1
Percentile formula
Lp= (n+1) x p/100
P is the percentile wanted
Mean absolute deviation
Σxi−x bar
/
N
Population variance
σ²=Σ(xi-μ)² / n
Sample variance
s²=Σ(xi−x bar)²/n-1
Standard deviation for population and sample variance
The root of the variance
Coefficient of variation function and formula
σ/μ or s/x bar
Used to measure variation relative to size of observations.
Chebyshev’s theorem
The proportion of value that lie within k standard deviations of the mean (for k>1) is at least 1-1/k squared.
E.g if k=2 at least 75% fall within +-2 population variance from mean.
Empirical/Normal rule
68% lies within +-curly A from mean
95% lies within +-2 curly A from mean
99.7% lies within +-3 curly A from mean
Bimodal distinction
2 or more peaks
Skewness measurement
Skewness (Sk)=3(mean-median)/s
S is sample standard deviation.
Sk is from -3 to 3
+-1 is moderate skewness
0 symmetric
Software coefficient of skewness
N/(n-1)(n-2) x (Σ(x-x bar)/s)
N is sample size
S is sample standard deviation
Correlation coefficient formula and function.
Shows strength of relationship.
Formula Best to remember by write down
R= sum of (X-mean of X)(Y-mean of Y) / (n-1) SxSy
Sx and Sy are standard deviations of x and y
Correlation coefficient range
-1 to 1
-1=perfect negative correlation
1=perfect positive correlation
Close to 0=no relationship.
