Ap Stat part 6

1st Quartile (Q1)

Is the median of the observations located to the left of the median in the ordered list.

What does this symbol stand for: σ

Population standard deviation.

Modified Box Plot

A data display that shows the five number summary.

Spread

A useful numerical description of a distribution.

Rule for Outliers

Call an observation an outlier if it falls more than 1.5x IQR above the third quartile or below the first quartile.

Five Number Summary

Consists of the smallest observation, the first quartile, the median, the third quartile, and the largest observation, written in order from smallest to largest.

When is the mean an appropriate measure of center

When the data is roughly symmetric.

When is the Median an appropriate measure of center

When the data is skewed left or right.

When is the Standard Deviation an Appropriate Measure of Spread

When there are no outliers and the graph is symmetric.

When is the Interquartile Range and Appropriate Measure of Spread

When there are outliers and skewness.

3rd Quartile (Q3)

Is the median of the observations located to the right of the median in the ordered list.

Median

Is the midpoint of a distribution, the number such that half of the observations are smaller and the other half are larger.

Types of Measures of Center

Mean and Median.

Resistant Measures

Median and IQR.

Types of Measures of Spread

Standard deviation and IQR.

What does this symbol stand for: µ

The population mean, the average score of the population on a given variable.

How to Calculate Q1

The 1st quartile is middle number of the values that are less than the median.

How to Calculate Q3

The 3rd quartile is the middle number of the values that are greater than the median.

What does this symbol stand for: ̅x

The mean.

Steps to Make a Boxplot

1. Draw and label a number line that includes the range of the distribution. 2. Draw a central box from Q1 to Q3. 3. Note the median M inside the box. 4. Extend lines (whiskers) from the box out to the minimum and maximum values that are not outliers.

Interquartile Range

Describes the middle 50% of values when ordered from lowest to highest.

What does this symbol stand for: Sx

Sample standard deviation.

Boxplot

The five-number summary divides the distribution roughly into quarters. Its also a new way to display quantitative data.

Mean

The most common measure of center is the ordinary arithmetic average.

Standard Deviation

The most common measure of spread looks at how far each observation is from the mean or the average distance.