DESCRIPTIVE STATISTICS
MODE
-
Most popular result
Any data type will work
MEDIAN
-
Central data point
Requires at least ordinal, preferably interval data quality
MEAN
-
Average score
Requires at least interval data quality
Sample
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𝑥̅ = mean
x = observations
n = number of observations
Population
𝜇=
𝜇 = mean
x = observations
n = number of observations
∑𝑥
𝑛
Calculator method
1. Reset mode
a. [SHIFT] +[MODE]+[3]+[=]+[AC]  clear all
b. [MODE]+[MODE]+[1]  SD mode
2. Insert units
a. [observation]+[SHIFT]+[,]+[frequency]+[M+]  5;3 for 3 observations of “5”
3. Calculate mean
a. [SHIFT]+[2]S-VAR+[1] 𝑥̅
VARIANCE
Sample
∑𝑛𝑖=1(𝑥𝑖 − 𝑥̅ )2
𝑠2 =
𝑛−1
S2 = variance for a sample
𝑥̅ = mean
n = number of values
Calculator method
1. Reset mode
2. Insert units
3. Calculate Standard Deviation
a. [SHIFT]+[2]S-VAR
i. [2]x𝜎n  Population SD
ii. [3] x𝜎n-1  Sample SD
4. Square result for variance
a. [ANS]+[x2]+[=]
Population
𝜎2 =
∑𝑛𝑖=1(𝑥𝑖 − 𝜇)2
𝑛
𝜎 2 = variance for a population
𝜇 = mean
n = number of values
STANDARD DEVIATION
-
Measure of spread of data
Sample
Population
𝑠 = √𝑠 2
S = standard deviation for a population
S2= variance for a population
𝜎 = √𝜎 2
𝜎= standard deviation for a population
𝜎 2 = variance for a population
Calculator method
1. Reset mode
2. Insert units
3. Calculate Standard Deviation
a. [SHIFT]+[2]S-VAR
i. [2]x𝜎n  Population SD
ii. [3] x𝜎n-1  Sample SD
COEFFICIENT OF VARIATION
-
Measure of spread relative to the scale of the mean
Best way to measure spread for non-negative data sets
Sample
𝑠
(100)
𝑥̅
S = standard deviation for a population
𝑥̅ = mean
Population
𝜎= standard deviation for a population
𝜇 = mean
-
FINDING OUTLIERS
Z – Score
- Only applicable to normal distributions
- Iterative process (i.e. can be done more than once)
- If z – score is greater than 3, observation is an outlier
𝑧𝑖 =
𝑥𝑖 − 𝑥̅
𝑠
Zi = z – score
Xi = observation to be tested
𝑥̅ = mean
S = standard devation
Box Plot
- MIN
o Q1 – 1.5(IQR)  IQR = Q3-Q1
- Q1
o Split again
- Median
o Central data point
- Q2
o Split again
- MAX
o Q3 + 1.5(IQR)
𝜎
(100)
𝜇
PROBABILITY
LAWS OF PROBABILITY
-
Sum of probabilities = 1
Probability of something not occurring is 1 – probability of it
occurring
INTERSECTION (both occur)
P(A∩B)
P(A’∩B)
P(B)
Union
P (AUB) = P (A) + P (B) - P (A∩B)
Conditional Probability
- Probability of A occuring, given that B already occurs
𝑃 (𝐴|𝐵) =
𝑃(𝐴 ∩ 𝐵)
𝑃(𝐵)
DEPENDANT/INDEPENDANT EVENTS
-
Calculated using Chi2 test
If Chi2 value > Chi Critical value, then events are dependant
Critical value requires degrees of freedom (# columns – 1)*(# rows – 1)
BINOMIAL PROBABILITY DISTRIBUTION
𝑓(𝑥 = 𝑎) = 𝑛𝐶𝑎 × 𝑝𝑎 × 𝑞 (𝑛−
P(A∩B’)
P(A’∩B’)
P(B’)
P(A)
P(A’)
1