if xi 's are the mid points of the class interval of grouped data,
fi 's are the corresponding frequinces
and
x^u is the mean,
then (sum of) fi( xi-x^u) is?
To find the sum of fi(xi - x^u), where xi's are the midpoints of the class interval of grouped data, fi's are the corresponding frequencies, and x^u is the mean, we need to follow these steps:
1. Calculate the deviation from the mean for each midpoint xi - x^u. This is done by subtracting the mean x^u from each midpoint xi.
2. Multiply each deviation (xi - x^u) by its corresponding frequency fi.
3. Add up all the products obtained in step 2 to find the sum of fi(xi - x^u).
Let's demonstrate this with an example:
Suppose we have the following grouped data:
xi (midpoints) | fi (frequencies)
---------------------------------------------
10 | 5
20 | 8
30 | 12
40 | 6
And let's assume the mean x^u is 25.
Step 1: Calculate the deviation from the mean for each midpoint xi - x^u.
For xi = 10, deviation = 10 - 25 = -15
For xi = 20, deviation = 20 - 25 = -5
For xi = 30, deviation = 30 - 25 = 5
For xi = 40, deviation = 40 - 25 = 15
Step 2: Multiply each deviation (xi - x^u) by its corresponding frequency fi.
For deviation -15, product = (-15) * 5 = -75
For deviation -5, product = (-5) * 8 = -40
For deviation 5, product = 5 * 12 = 60
For deviation 15, product = 15 * 6 = 90
Step 3: Add up all the products obtained in step 2.
Sum of fi(xi - x^u) = -75 + (-40) + 60 + 90 = 35
Therefore, the sum of fi(xi - x^u) for the given data is 35.