Lecture 3 - Descriptive Statistics 1-2 (9/29-10/1)

X (capital)

all possible values of the random variable

x (lowercase)

a specific value of X that was measured

Parameter

A fixed numerical characteristic of the population

ex: population mean, proportion, and standard deviation

Statistic

A numerical characteristic computed from a sample

ex: sample mean, proportion, and standard deviation

Measure of the center

Describes the typical or central value in a dataset

Sample mean

x̅ (x bar), the average

A measure of center

Median

x̃ (x tilde), describe the 50th percentile of the data

Percentile

X_p, where 0 < P < 100. P% of the data lies below it and (100-P)% of the data is above. So if you were 97th percentile in a class that means that 97% of students did worse than you

What is this for and how do you use it?

This is for seeing which data point is at the pth percentile

P = percentile

n = the number of individuals

If you get a decimal, take the average of the individuals on either side of the decimal

Range

The overall span of the data

Interquartile range (IQR)

The spread of the middle half of the data (Q3-Q1)

Sample variance

The average of the squared deviations from the mean

Sample standard deviation

A measure of how far values typically are from the mean

(the square root of sample variance)

Frequency in descriptive statistics for categorical data

The number of sample items that fall into each category

Relative frequency/sample proportions in descriptive statistics for categorical data

The frequency of a category is divided by total sample size

The fraction or percentage of the sample in each category