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

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:

○ ヌ 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.