MATH 140 Ch 2

Median

Midpoint of the distribution. Least affected by outliers. for odd numbers 843 + 1/2 = 421

Five-number summary

Minimum Q1 M Q3 Maximum

Boxplots

The five-number summary divides the distribution roughly into quarters. This leads to a new way to display quantitative data, the boxplot.

Interquartile range

Q3 - Q1 In addition to serving as a measure of spread, the interquartile range (IQR) is used as part of a rule of thumb for identifying outliers. The 1.5 IQR Rule for Outliers Call an observation a suspected outlier if it falls more than 1.5 IQR above the third quartile or below the first quartile.

Mean (x̅)

The average of the distribtuion. It is not a resistant measure of center, outliers can affect the value.

Measuring spread: standard deviation

The standard deviation, s, is the square root of the variance, s2

The median and IQR are usually better than the mean and standard deviation for describing

a skewed distribution or a distribution with outliers.

Measuring the spread : quartiles

contains 50% of the data within the distribution.

how do you measure the center of a distribution

mean (x̅) or median (M)

Choosing measures of center and spread

mean and standard deviation OR median and interquartile range

s (standard deviation) and _𝑥_ (mean) are used only with

normal (bell shaped) distribution.

Variance

of a set of n observations is denoted by s2 s^2 = 1/n-1 Σ (xi-x̅)^2