In equation form what is the Cumulative Frequency Function for a histogram and what does it mean?

Answer 1

mi= summation (mj) is the equation and it means that it counts all the observations together.

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Clear as mud!

Suppose you have a variable X that can take the values xi and that x1<x2< ... < xn.

And you have a frequency distribution function

f(xi) = mi for each value of i

Then

the cumulative frequency distribution is

F(xk) = f(x1)+f(x2) + ... +f(xk) = m1+m2+...mk

that is, F(xk) is the sum of all the frequencies up to and including k.

In other words, it is the number of times (frequency) that the result was less than or equal to xk.