Notes - Matwa - F2P Formulas

Chapter 1: Statistika

Rata-Rata (Mean)

x=(∑_^)((x_i))/n

For ungrouped data, the mean is simply the sum of all elements divided by the number of elements.

x=(∑_^)((ƒ_i)⋅(x_i))/(∑_^)((ƒ_i))

For grouped data, the mean is the sum of all groups' frequencies multiplied by their midpoints (x_i) divided by the sum of the frequencies (how many data points there are)

Median, Kuartil, Desil, etc.

Median=(x_(n+1)/2)∨((x_n/2)+(x_n/2+1))/2

(P_k)=(x_(k/100)*(n+1))

(D_k)=(x_(k/10)*(n+1))

(Q_k)=(x_(k/4)*(n+1))

The median is the middle element. Arrange data in ascending order first. For ungrouped data, use the first option if n is odd, and the second if it's even.

For the percentile, decile, and quartile, use the above formulae. If the index of (x_i) is a fraction, just interpolate between the 2 values. For example, if I get (x_3.3), then the answer would be (x_3)+((x_4)-(x_3))⋅0.3

Median=L+(N/2-F)/ƒ⋅c

(P_k)=L+((k*N)/100-F)/ƒ⋅c

(D_k)=L+((k*N)/10-F)/ƒ⋅c

(Q_k)=L+((k*N)/4-F)/ƒ⋅c

For grouped datasets, the formula is more complicated. First, you need to find the class/group that the value belongs to. You can find the index of said value via the (k*N)/x part. Then, simply plug in L the lower bound of the class, F the cumulative frequency of the class before the class containing the target value, ƒ the frequency of the found class, and c the width of the class.

If you're confused, let's have an example. Let's say the median is at value 67, and the cumulative frequency sum before the class is 60. This means the values is at number 67-60=7 in the class. Divide that by ƒ to find the "7 out of how many values", then multiply by c and add by L to get the value.

One caveat to the formulae is that the base formula only works for continuous classes, for example 1-10,10-20,20-30. For non-continuous classes like 1-9,10-19,20-29, simply add/subtract 0.5 to either end of the class, for the class 20-29 that means L would be 19.5 and c would be 10