Measure of Central Tendency

Question 1

Arithmetic Mean
i] Discrete
ii] Discrete with frequency
iii] Grouped Discrete data with frequency.

Answer 1

I] E xi /n
ii] E xifi / Efi
iii] A + E df /Ef x h ; A is assumed mean and H is class length. d= X - A / h

Question 2

Sum of Deviation of a set of observations from their AM is

Answer 2

E(xi - /x) = 0
Efi(xi -/x) = 0

Question 3

AM is affected by change of origin and Change of scale then Formula

Answer 3

y = a +bx

Question 4

Combined AM

Answer 4

n1x1 + n2x2 /n1 + n2

Question 5

Median
Discrete
1. ODD
2. EVEN

Answer 5

1. (n+1/2 )th Observation
2. (n/2) th observation + (n/2+1) th observation / 2

Question 6

Median Continuous

Answer 6

l + N/2 - CF / f x c ; l - lower limit , Cf - preceding CF , h- Class interval

Question 7

Discontinuous [ add or sub amount]

Answer 7

half of the discontinuous amount

Question 8

Median if x and y are two variables

Answer 8

y = a+bx

Question 9

Deviations in Median

Answer 9

E|x-A| is minimum

Question 10

Q,D,P

Answer 10

___ observation + 0.___ x Difference between the ___ and ___ values .

Q= 1/ 4
d = 1/10
p = 1/100

Question 11

mode

Answer 11

l [ f0 -f-1/ 2f0 - f-1 - f1] x C ;

l LCB model class ;
f0 - frequency of the modal class
f1 - Frequency of post modal class
f-1 - Frequency of pre modal class
C - class length of the Modal class

Question 12

Mode with respect to median and Mean

Answer 12

Mean - Mode = 3(mean - Median)

Question 13

GM formula

Answer 13

( x1 * x2x3x4…xn) 1/n

Question 14

GM properties

1. if all the properties of GM are k
2. GM of z =

Answer 14

1. k
2. GM of x * GM of y

Question 15

Harmonic mean formula and Properties

Answer 15

n / E(1/x)

Grouped data
N/E[f/x]

If all the observations are taken as K, HM is K

n1+n2/ n1/h1 + n2/h2

Question 16

Mode is affected by ?

Answer 16

Sampling fluctuations and not by mathematical property

Question 17

Dispersion

Meaning ?

Answer 17

Amount of deviation from central frequency

Question 18

Measure of Dispersion

Absolute measures

Answer 18

Range
MD
QD
SD

Question 19

Measure of Dispersion

Relative Measures

Answer 19

Coefficient of Range
Coefficient of MD
Coefficient of QD
Coefficient of SD

Question 20

Range

Meaning
formulas

Answer 20

For every grouped / ungrouped data
Range = Largest - Smallest

Coefficient of Range = L - S / L+ S x 100

Question 21

Mean Deviation

Ungrouped data
1. Mean
2. Median
3. Assumed Mean

Answer 21

1. E|x-x’|/n
2. E|x-M|/n
3. E|x-A|/n

Question 22

Mean Deviation

Grouped Data [Both discrete and continuous]

1. Mean
2. Median
3. Assumed Mean

and coefficient of MD

Answer 22

1. Ef(x-x’) / n
2. Ef(x-M) / n
3. Ef(x-A) / n

Coefficient of MD
1. mean - MD about X’/x’ * 100
2. Median - MD about A / A * 100
3. Assumed Mean - MD about M / M * 100

Question 23

Standard Deviation

Meaning

For Ungrouped Data
For Grouped Data

Answer 23

It takes AM , Best Measure of Dispersion

Un Grouped Data
SD = Square root (Ex^2/n - (X’)^2) , X’ = Ex/n

or

SD = Square root (E(x-x’)^2 / n)

Grouped data
SD = Square root (Efx^2/N - (X’) ^2)

Question 24

Properties of SD

Answer 24

SD of any 2 no’s A and B

SD of a and b = |a-b/2| = Range /2

SD remain unaltered on Shift of origin
-> If You add/Subract a number with all the x nothing will change

SD remain altered on Shift of Scale
-> Multiplying/ Dividing same number with all the no of X things

Question 25

SD of First “n” natural Numbers

Answer 25

Square Root (n^2 -1 /12)

Question 26

Variance =

Answer 26

Variance = (SD) ^2

[Square root [ E (x-x’)^2/n] = E(x-x’)^2 /n

Question 27

Coefficient of variation [CV]

a. Lesser CV _______ consistency
b. Greater CV ________ Consistency

Where CV used?

Answer 27

SD / AM * 100

a. Greater Consistency
b. Worst Consistency

CV is a statistical tool to test the consistency of the data

Question 28

combined SD

Answer 28

Square Root ( n1s1^2 + n2 S2^2 + n1d1 ^2 + n2d2 ^2 / n1+n2)

d1 ^2 = (X’1 - X’c) ^2
d2^2 = (X’2 - X’c) ^2 ,,

X’c = Combined Mean
X’c = n1x1’ + n2x2’ /n1+n2

Question 29

QD - Quartile Deviation

Meaning

QD - formula

Coefficient of QD

Answer 29

Appropriate measure of dispersion for open end classification

QD = Q3 - Q1 / 2

Q3 -Q1 = Inter Quartile Range

Q3-Q1/2 = Semi Inter Quartile Range

Coefficient of QD = Q3 - Q1 /Q3+Q1 x 100

or QD / M * 100 , M -> Median

Question 30

Relationship between SD , MD , QD

Answer 30

SD > MD > QD

Example
2SD = 2.5MD = 3QD

if it’s all are equated so one having highest multiplier is smallest and One having lowest Multiplier is biggest

Question 31

x and y are 2 variable as ax + by + c =0
with dispersion of x then

Answer 31

dispersion of y = |a/b| * Dispersion of X

Question 32

Best Measure of central tendency without any conditions

Answer 32

AM

Question 33

Best measure
Positional average

Answer 33

median

Question 34

For Open end classification best measure

Answer 34

Median and partition

Question 35

Which means of central tendency are suitable for % and Ratios

Answer 35

GM

Question 36

Which are ratios

Answer 36

HM and GM