Week 1 Chapter 3: Univariate Population Parameters and Sample Statistics

Summation Notation ∑ meaning

Sum of all data/numbers

Summation Notation example

X=7,11,18,20,24

∑X=7+11+18+20+24

∑X=80

Xi meaning (little i)

identifies which observation you're talking about

Score for variable X for a particular individual or object

Xi example

X1=7

The first person's X score is 7

∑Xi​ meaning

Add all x scores

Central Tendancy

Where is the center of the data?

Mean, median, mode

Central Tendency: Mode

Value that appears most frequently in a dataset, most useful

Appropriate for nominal, ordinal, interval, ratio (only one appropriate for nominal)

Central Tendency: Mode example

2, 3, 3, 3, 4, 5, 5

Mode=3

Central Tendency: Median

The middle value when the data is arranged in ascending or descending order.

Separates lower and upper half of the data.

Less affected by extreme values and is useful with skewed distribution

Central Tendency: Median example

2, 5, 7, 9, 12

Median=7

Central Tendency: Median example with even amount of numbers

2, 5, 7, 9, 12

Middle=7,9

(7+9)/2 = 16/2

=8

Central Tendency: Mean

The average of the data

Summing up all values and dividing by number of values.

Represents the balance point of distribution and is sensitive to outliers

Central Tendency: Mean example

5, 7, 8, 10

5+7+8+10=30

n=4

Xˉ=430​

Xˉ=7.5

Measures of Central Tendency: Mode

Unimodal, bimodal distributions