Statistics, Chapter 2: Describing and Exploring Data

Line Graphs

• Best for time series or data measured over intervals.

• Show trends and changes over time.

Bar Graphs

• Display categorical data.

• Bars do not touch.

• Height of each bar shows frequency or relative frequency.

Histograms

• Used for quantitative (numerical) data.

• Bars touch to represent continuous intervals.

• Show shape, center, and spread of distribution.

Frequency Polyglon

Connects midpoints of histogram intervals with straight lines. 

Time-series Graph

Plots data points in order over time.

Mean

Arithmetic average. Sensitive to outliers.

Median

Middle value when data are ordered. Resistant to outliers.

Mode

Most frequently occurring value. Useful for categorical data.

Range

Max-minimum. Sensitive to outliers.

IQR

Spread of the middle 50% of values. Resistant to outliers.

Standard deviation

Average distance of data values from the mean.

Variance

Square of the standard deviation.

What type of data does a histogram display?

Quantitative (numeric) data; shows distribution.

What type of data does a bar graph display?

Categorical data

What does a box plot display

The 5-number summary (min, Q1, median, Q3, max) outliers.

What does a gap in a histogram mean vs. a gap in a bar graph?

Histogram gap = no values in that interval.

Bar graph gap = no individuals in that category.

When is mean the better measure of center?

Symmetric distribution with no outliers.

When is median the better measure of center?

Skewed distribution of when outliers are present.

Which is more affected by outliers: mean or median?

Mean is.

In a right skewed distribution, how do mean and median compare?

Mean > median

In a left-skewed distribution, how do mean and median compare?

Mean < Median

In a symmetric distribution, how do mean and median compare?

Mean = median

Which measure of spread is resistant to outliers?

IQR (interquartile range)

Which measures of spread are not resistant to outliers?

Range, standard deviation, variance

What is the formula for detecting outliers with IQR?

Below Q1 - 1.5 x IQR or above Q3 + 1.5 x IQR

How are outliers shown on a box plot?

As points/dots beyond the whiskers.

Why are outliers so important to notice?

They may represent unusual cases, errors, or natural variation, and they can distort mean and standard deviation.