CHAPTER 7: Measures of Location Flashcards
Define measures of position/location (aka fractile/quantile)
Indicates the relative position of an observation in an array based on the percentage of values less than or equal to the observation
Give an example of a commonly used measure of location
Median - at least 50% of the observations have values less than or equal to the median and at least 50% of the observations have values greater than or equal to the median
What is the minimum level of measurement for measures of location?
Ordinal
Define percentiles
Divides ordered observations into 100 equal parts, has 99 percentiles
How are percentiles interpreted?
“The kth percentile, Pk, is a value where at least k% of the observations are less than or equal to it and at least (100-k)% are greater than or equal to it”; (k = 1, 2, …, 99)
ex.
The 1st percentile (P1) is a value such that at least 1% of the observations are less than or equal to it and at least 99% of the observations are greater than or equal to it
Interpret if the 39th percentile has a value of 15
At least 39% of observations are less than or equal to 15 and at least 61% are greater than or equal to 15
What does the percentile score/rank determine
Determines the position of an observation wherein:
a(100) percentile score indicates that at least a(100%) of all scores in a collection are less than or equal to the individual’s score and at least (1-a)(100%)
Interpret the percentile score if Juan’s percentile score is 95.5
At least 95.5% of other students’ scores are less than or equal to Juan’s score, and at least 4.5% of other students’ scores are greater than or equal to Juan’s score.
If there are 50 students: (50)(4.5%) = 2.25 or 2 will not exceed Juan’s score
Differentiate the percentile score and percentage score
The percentile score is the relative score compared to the rest of the data while the percentage score is an individual score out of 100.
How to compute the percentage score
(total score/total number of points) * 100 = %
ex.
Total score: 19, total number of points: 120
Percentage score = (90/120) * 100 = 75%
When is Pk interpolated
When (nk)/100 is an integer
How does the Empirical Distribution Number with Averaging (EDNA) determine the kth percentile?
Arrange n observations in an array, where the ith observation is X(i)
Compute for (nk)/100
Case 1: if (nk)/100 => integer
Pk = [X(nk/100) + X((nk/100) + 1)] / 2
Case 2: if (nk)/100 => not an integer
Pk = X([nk/100]+1)
How does the Weighted Average Estimate determine the kth percentile?
Arrange n observations in an array, where the ith observation is X(I)
Compute for [(n+1)k] / 100 = j + g, where j is the integer and g is the fractional (decimal) part
Determine Pk by linear interpolation:
Pk = (1-g)X(j) + g(j+1)
Pk = X(j) + g*[X(j+1) - X(j)]
How is the percentile approximated from the FDT?
Compute for (nk)/100
Construct the <CFD
Locate the kth percentile class (Pkth class), which is the class interval where the <CF is greater than or equal to (nk)/100 for the first time starting from the top
Compute using formula:
Pk = LCBPk + C * [(nk/100 -<CFDPk-1) / fPk]
What are quartiles
Measures of location that divide an array into 4 parts, has 3 quartiles
