Statistics — Formula Sheet

x̄ = (f1x1 + f2x2 + ... + fnxn) / (f1 + f2 + ... + fn)

x̄ = (Σfi xi) / (Σfi)

Class mark = (Upper class limit + Lower class limit) / 2

di = xi - a

x̄ = a + (Σfi di) / (Σfi)

Mode = l + ((f1 - f0) / (2f1 - f0 - f2)) × h

Median (M) = l + (((n / 2) - cf) / f) × h

For ungrouped data, if n is odd, median is the ((n+1)/2)th observation

For ungrouped data, if n is even, median is average of the (n/2)th and (n/2 + 1)th observations

Example 1 exact mean = 59.3.

Example 1 grouped mean = 62.

This method uses \(u_i = (x_i - a)/h\), where \(h\) is the class size or a suitable divisor.