Question

How to find the arithmetic mean with a frequency table

Answer 1

$answer❤️$

It is easy to calculate the Mean: Add up all the numbers, then divide by how many numbers there are.

here ex :-

But sometimes we don't have a simple list of numbers, it might be a frequency table like this (the "frequency" says how often they occur):

Score Frequency

1=2

2=5

3=4

4=2

5=1

(it says that score 1 occurred 2 times, score 2 occurred 5 times, etc)

We could list all the numbers like this:

Mean =

1+1 + 2+2+2+2+2 + 3+3+3+3 + 4+4 + 5

(how many numbers)

But rather than do lots of adds (like 3+3+3+3) it is easier to use multiplication:

Mean =

2×1 + 5×2 + 4×3 + 2×4 + 1×5

(how many numbers)

And rather than count how many numbers there are, we can add up the frequencies:

Mean =

2×1 + 5×2 + 4×3 + 2×4 + 1×5

2 + 5 + 4 + 2 + 1

And now we calculate:

Mean =

2 + 10 + 12 + 8 + 5

14=3714= 2.64...

And that is how to calculate the mean from a frequency table!