The shortcut method to find out the mean of large frequencies data is
The shortcut method to find out the mean of large frequencies data is Correct Answer A + h∑f<sub>i</sub>u<sub>i</sub>/N
Explanation
Mean = Sum of all observation/ Numbers of observations
For example the mean of 2, 4, 6 is
⇒ (2 + 4 + 6)/3
∴ Mean = 4
The direct method to solve these frequency data completely fail so we use short cut method to solve mean of the data. Here we shifted the origin to some point A( xi - A) which is called di as deviation from point A
⇒ di = xi - A
⇒ xI = di + A
Mean = ∑ fixi/∑ fi = ∑fi(di + A)/∑fi
⇒ /∑fi
⇒ ∑fidi/∑fi + A or A + ∑fidi/∑fi
Assumed value + Mean of the new variate ‘d’
When data is in equal class interval we can reduced the deviation by divide (xi – A)/h
⇒ ui = (xi – A)/h
⇒ u i = di/h
⇒ di = ui × h
⇒ x̅ = A + ∑fihui/∑fi
⇒ N = ∑fi
∴ The shortcut method to solve the mean of large frequencies data is x̅ = A + h∑ fiui/N