Measures of the Location of the Data

Quartiles

the numbers that separate the data into quarters; quartiles may or may not be part of the data. The second quartile is the median of the data.

What does a percentile indicate?

the relative standing of a data value when data are sorted into numerical order from smallest to largest. Percentages of data values are less than or equal to the pth percentile. For example, 15% of data values are less than or equal to the 15th percentile. Low percentiles always correspond to lower data values. High percentiles always correspond to higher data values.

A formula for calculating the k th percentile. Here is one of them: k = the kth percentile, it may or may not be part of the data i = the index, ranking or position of a data value, n = the total number of data

i = k/100 * (n+1)

A Formula for Finding the Percentile of a Value in a Data Set. Order the data from smallest to largest: x = the number of data values counting from the bottom of the data list up to but not including the data value for which you want to find the percentile, y = the number of data values equal to the data value for which you want to find the percentile, n = the total number of data

(x + 0.5y)/n * (100)

first quartile or Q1

One-fourth, 25%, of the ordered data set are less than the Q1

third quartile or Q3

Three-fourths, 75%, of the ordered data set are less than the Q3

Percentile

a number that divides ordered data into hundredths; percentiles may or may not be part of the data. The median of the data is the second quartile and the 50th percentile. The first and third quartiles are the 25th and the 75th percentiles, respectively.

median

a number that measures the "center" of the data; You can think of it as the "middle value," but it does not actually have to be one of the observed values. It is a number that separates ordered data into halves. Half the values are the same number or smaller than the median, and half the values are the same number or larger.

second quartile or Q2

also known as the median; it separates the ordered data set into two equal halves, 50%.

Outlier

an observation that does not fit the rest of the data; A value is suspected to be a potential outlier if it is less than 1.5 IQR below the first quartile or more than 1.5 IQR above the third quartile.

When writing the interpretation of a percentile in the context of the given data, the sentence should contain what 4 pieces of information?

information about the context of the situation being considered; the data value (value of the variable) that represents the percentile; the percent of individuals or items with data values below the percentile; the percent of individuals or items with data values above the percentile.

Interquartile Range

or IQR, is the range of the middle 50% of the data values; the IQR is found by subtracting the first quartile from the third quartile. It is the difference between the third quartile Q 3 and the first quartile Q 1. IQR = Q 3 - Q 1