2.1 – Describing Location in a Distribution

Day 1 on Assignment Guide

Percentiles

• The percent of observations in a set of data that are below a certain value.

• It is possible to include equal to, but we will strictly do below for consistency

Cumulative Relative Frequency Plot

• Remember relative frequency is percent• Cumulative – running total

AKA “Ogives”

Shape for Cumulative Relative Frequency Plot

Where is the graph the steepest?

What does this mean?

Sketch a Cumulative Relative Frequency Plot for

this data. Describe the shape.

Sketch a Cumulative Relative Frequency Plot for symmetric and skewed left

Check Your Understanding

Turn to page 89 and do problems 1 – 4We will do one at a time on the whiteboards

z-scores

• Also called standardized value• It is unit-less• Tells us how many standard deviations away

from the mean a particular value is• Formula is on your formula sheet and on p. 90

In 2009, the mean number of wins in MLB was 81 with a standard deviation of 11.4 wins.

1. Find and interpret the z-score for the NY Yankees if they had 103 wins.

2. Find and interpret the z-score for the NY Mets if they had 70 wins.

1. z-score = (103-81)/11.4 = 1.93. Interpret: The NY Yankees were 1.93 standard deviations above the mean number of wins.

2. z-score = (70-81)/11.4 = -0.96. Interpret: The NY Mets were 0.96 standard deviations below the mean number of wins.