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Department of Geodesy & Geomatics Engineering

Deskripsi Data

Heri Sutanta

Central Tendency

• Many data sets have a distinct central tendency with the data values grouped or clustered around a central point

• Everyday expression: average value, middle value, most popular or frequent value

• Variation measures the spread or dispersion of values in a data set

• One simple measure of variation is range: the difference between the lowest and the highest value

Heri Sutanta Department of Geodesy & Geomatics Engineering, UGM

Range

• Range is equal to the largest values minus the smallest value


Mean

• The arithmetic mean (the mean) is the most common measure of central tendency

• Extreme value?


Median

• The median is the value that partition or splits and ordered set of data into two equal parts

• It is not affected by extreme values• The median is the middle value in a set of data

that has been ordered from lowest to highest value– Rule 1 If there is an odd number of values in the data

set, the median is the middle-ranked value– Rule 2 If there is an even number of values in the data

set, the median is the mean of the two middle-ranked value


Mode

• The mode is the value in a data set that appears most frequently

• Extreme values do not affect the mode• Should only be used for descriptive purposes as

it is more variable than either the mean or the median

• Often there is no mode or there are several modes in the data set


Quartiles

• Quartiles divide a set of data into quarters, that is, four equal parts– First quartile, Q1: 25% values are smaller or equal to

Q1. Q1 = (n+1) / 4

– Second quartile, Q2: is the median

– Third quartile, Q3: 75% values are smaller or equal to Q3. Q3 = 3(n+1) / 4


Quartiles

• Rule 1 If the result is an integer, then the quartile is equal to the ranked value. n = 7, Q1?– Q1 = (7+1) / 4 = second ranked value

• Rule 2 If the result is a fractional half (2.5, 3.5, 7.5, etc.) then the quartile is equal to the mean of the ranked value. n = 9, Q1?– Q1 = (9+1) / 4 = 2.5 ranked value, halfway between

the 2nd and 3rd ranked value


Quartiles

• Rule 3 If the result is neither an integer nor a fractional half, round the result to the nearest integer and select that ranked value. n = 10, Q1?– Q1 = (10+1) / 4 =2.75 ranked value. Round 2.75 to 3

and use the 3rd ranked value


Interquartile Range

• Interquartile range is the difference between the third and the first quartile

– Interquartile Range = Q3 – Q1


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