Averages Of First Order Flashcards
Most common first order averages are
Mean
Median
Mode
Mean
Quotient of sum of all values of given data and the number if values of data
Methods of mean
Direct
Indirect
Step-deviation
Formula for direct method ungrouped data
__
X=€x
——
N
Formula for direct method grouped data
__
X=€fx
——
€f
Formula for indirect method ungrouped
__
X=A+€D
——
N
Formula for indirect method grouped data
__
X=A+€fD
——
€f
Formula for step deviation ungrouped data
__
X=A+€u *c
—–
N
Formula for step deviation grouped data
__
X=A+€fu *c or h
——
€f
What is change of origin
When we take D we subtract a constant from every value of the given data, this step is called change of origin
What is change of scale
When we take u, we divide D by h or c, this step is called change of scale
Weighted arithmetic mean
Arithmetic mean computed for different items by considering relative importance of each item
Formula for weighted arithmetic mean
__
Xw=€WX
———
€W
What are the strengths of arithmetic mean
Simple to understand and easy to calculate
Utilises all the values given in the data
Finite in every case
What are the weaknesses of arithmetic mean
Greatly affected by extreme values
Cannot be calculated for qualitative data
Can not be exactly calculated for open and distribution
Mode
Most repeated value of data
Formula for mode in continuous variable grouped
X=L+(fm-f1)
———————*h
(Fm-f1)+(fm-f2)
Graphical method of locating mode
Histogram
What are the advantages of mode
Positional average
Easy to understand
Not affected by large or small values
What are the weaknesses of mode
Not rigidly defined by the mathematical formula
May not exist in some cases
Has no use in statistical treatment of data
Median
Exact central value or observation of an array data
Formula for grouped data median in continuous variable
~
X=L+h/f(n/2 -CF)
Graphical method of locating median
Ogive
What are the advantages of median
Simple to understand and simple to obtain
Notification by extreme values
Can be computed exactly
What are the weaknesses of median
Cannot be simply calculated by the mathematical formula
Less commonly used
Not best suited for further statistical treatment
What is symmetrical data distribution
A distribution by its shape is called symmetrical distribution if both the tails of its frequency curve are equally extended on both sides from the centre
What is Moderately skewed data
A distribution is called skewed either positive skewed or negative skewed by its shape if both the tails of the frequency curve are not equally extended on both sides from the centre. The distribution is called positive if the right tail of the curve is more extended than the left. And negative if vice versa
Relationship between the three averages in moderately skewed distribution
Mode= 3 median -2 mean
Qualities of a good average
Utilises all the values given in the data
Not much affected by the extreme values
Mathematically defined
Can be calculated in almost all cases
