LECTURE: AL MUIZZUDDIN F., SE., ME..  2 Apa itu Variasi?

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Presentation transcript:

LECTURE: AL MUIZZUDDIN F., SE., ME.

 2 Apa itu Variasi?

  Range  Standar Deviasi 3 Pengukuran Variasi

 4 Range Because the range uses only the maximum and the minimum data values, it is very sensitive to extreme values and isn’t as useful as other measures of variation that use every data value, such as the standard deviation.

 5

 6 Standard Deviation of a Sample

 7

  The following properties are consequences of the way in which the standard deviation is defined:  The standard deviation is a measure of variation of all values from the mean.  The value of the standard deviation s is usually positive. It is zero only when all of the data values are the same number. (It is never negative.) Also, larger values of s indicate greater amounts of variation.  The value of the standard deviation s can increase dramatically with the inclusion of one or more outliers (data values that are very far away from all of the others).  The units of the standard deviation s (such as minutes, feet, pounds, and so on) are the same as the units of the original data values. 8 Next

 9

 10

 11

 12 Standard Deviation of a Population

 13 Variance of a Sample and a Population

  One crude but simple tool for understanding standard deviation is the range rule of thumb, which is based on the principle that for many data sets, the vast majority (such as 95%) of sample values lie within two standard deviations of the mean. 14 Beyond the Basics of Variation

 15 Range Rule of Thumb

 16

 17

 18 Rule for Data with a Bell-Shaped Distribution

 19 Figure 3.3

 20

 21 Latihan Soal 1 Carilah nilai mean, varian, dan std deviasi!

 22 Latihan Soal 2

 23