The arithmetic mean is the best measure of central tendency because:
The arithmetic mean is the best measure of central tendency because: Correct Answer All the above
Explanation
The arithmetic mean is the most important measure of central tendency. it is also known as average but in statistics it is called arithmetic mean.
The arithmetic mean defines as the sum of the items divided by the number of items. The arithmetic mean gives us the most stable measure and
it is easy to calculate and in arithmetic mean we considered all the observation.
∴ All of the above is the correct answer of this question
Important Points
There are various measure of central tendency
1 - Arithmetic mean
The arithmetic mean is denotted by X̅ is given by
X̅ = (x1 + x2 + ------ xn)/n
X̅ = ∑xi/n
Where as (x1 + x2 + ------ xn) are observations
n = Number of observation
2 - Geometric mean
The geometric mean is defined as the Nth square root of product of N observations and geometric mean is denotted by G
G = N√x1 × x2 × --------xN)
3 - Harmonic mean
The harmonic mean is the reciprocal of the arithmetic mean. The HM of N observation x1, x2, -----xN is
H = 1/1/N∑(1/xi) or N/∑(1/xi)
4 - Median
The median is the central value of the average of the data.Median is denotted by M
M = (N + 1)/2)th item
The median of the grouped classes
Median = L + (N/2 - C)/F × H for group data
L = lower class limit of the median class
N = total frequency
C = cumulative frequency of the pre median class
F = frequency of the median class
H = width of median class
5 - Mode
Mode is that point where the frequencies in distribution are maximum.
The Mode in a grouped data is given by
Mode = L + × i
i = class interval or class size
f1 = frequency of modal class
fo = frequency of pre modal class
f2 = frequency of success modal class
L = lower limit of modal class
