Averages Of First Order

Question 1

Most common first order averages are

Answer 1

Mean
Median
Mode

Question 2

Mean

Answer 2

Quotient of sum of all values of given data and the number if values of data

Question 3

Methods of mean

Answer 3

Direct
Indirect
Step-deviation

Question 4

Formula for direct method ungrouped data

Answer 4

__
X=€x
——
N

Question 5

Formula for direct method grouped data

Answer 5

__
X=€fx
——
€f

Question 6

Formula for indirect method ungrouped

Answer 6

__
X=A+€D
——
N

Question 7

Formula for indirect method grouped data

Answer 7

__
X=A+€fD
——
€f

Question 8

Formula for step deviation ungrouped data

Answer 8

__
X=A+€u *c
—–
N

Question 9

Formula for step deviation grouped data

Answer 9

__
X=A+€fu *c or h
——
€f

Question 10

What is change of origin

Answer 10

When we take D we subtract a constant from every value of the given data, this step is called change of origin

Question 11

What is change of scale

Answer 11

When we take u, we divide D by h or c, this step is called change of scale

Question 12

Weighted arithmetic mean

Answer 12

Arithmetic mean computed for different items by considering relative importance of each item

Question 13

Formula for weighted arithmetic mean

Answer 13

__
Xw=€WX
———
€W

Question 14

What are the strengths of arithmetic mean

Answer 14

Simple to understand and easy to calculate
Utilises all the values given in the data
Finite in every case

Question 15

What are the weaknesses of arithmetic mean

Answer 15

Greatly affected by extreme values
Cannot be calculated for qualitative data
Can not be exactly calculated for open and distribution

Question 16

Mode

Answer 16

Most repeated value of data

Question 17

Formula for mode in continuous variable grouped

Answer 17

X=L+(fm-f1)
———————*h
(Fm-f1)+(fm-f2)

Question 18

Graphical method of locating mode

Answer 18

Histogram

Question 19

What are the advantages of mode

Answer 19

Positional average
Easy to understand
Not affected by large or small values

Question 20

What are the weaknesses of mode

Answer 20

Not rigidly defined by the mathematical formula
May not exist in some cases
Has no use in statistical treatment of data

Question 21

Median

Answer 21

Exact central value or observation of an array data

Question 22

Formula for grouped data median in continuous variable

Answer 22

~

X=L+h/f(n/2 -CF)

Question 23

Graphical method of locating median

Answer 23

Ogive

Question 24

What are the advantages of median

Answer 24

Simple to understand and simple to obtain
Notification by extreme values
Can be computed exactly

Question 25

What are the weaknesses of median

Answer 25

Cannot be simply calculated by the mathematical formula
Less commonly used
Not best suited for further statistical treatment

Question 26

What is symmetrical data distribution

Answer 26

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

Question 27

What is Moderately skewed data

Answer 27

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

Question 28

Relationship between the three averages in moderately skewed distribution

Answer 28

Mode= 3 median -2 mean

Question 29

Qualities of a good average

Answer 29

Utilises all the values given in the data
Not much affected by the extreme values
Mathematically defined
Can be calculated in almost all cases