APST 207 Lecture Notes - Lecture 4: Squared Deviations From The Mean, Standard Score

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10 Feb 2017
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Descriptive Statistics
Some Symbols
We use symbols in stats to make our lives easier
Symbols we know:
N- number of cases in a population
N- number of cases in a sample
A new symbol: Σ sigma
Means “sum everything that comes after the symbol
So.. xi means add up all the values for x (or all the data points,where x is the
variable and i is every single case
Sum Symbols
Suppose we have these data points: 1,2,2,3,3,3
xi = 1 +2+2+3+3+3=14
xi =12 +22+22+32+32+32+36
(xi)2 = (1+2+2+3+3+3)2=196
Mean
Mean (average)- the typical value in a dataset
Calculated by summing all values of x in the dataset (we call this x1) and dividing
it by the number of cases in the dataset. Symbolically we show this as:
Pros:
for all cases
Cons
Sensitive to extreme values (e.g household)
Excel function: =Average()
Then select the range of values
Measures of Dispersion
Range, Variance, and Standard Deviation
Range
Range: the largest value minus the smallest value
Simplest measure of dispersion
Pros: Applies to any size dataset
Cons =: Very sensitive to extreme values
Ex: 2,8,9,14,21,83
Range: 83-2=81
Excel has no Range function!!
Use=Max()-Min()
Input the data range for both Min and Max
Variance
Variance: How “spread out” the data is
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Document Summary

We use symbols in stats to make our lives easier. N- number of cases in a population. N- number of cases in a sample. Means sum everything that comes after the symbol. So xi means add up all the values for x (or all the data points,where x is the variable and i is every single case. Suppose we have these data points: 1,2,2,3,3,3. Mean (average)- the typical value in a dataset. Calculated by summing all values of x in the dataset (we call this x1) and dividing it by the number of cases in the dataset. Range: the largest value minus the smallest value. Cons =: very sensitive to extreme values. Input the data range for both min and max. Variance: how spread out the data is. On average,how much the cases deviate from the mean. Divided by the sample size (n) minus 1 - or- The average of the squared deviations from the mean.

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