Question

Data: 7,-5, -8, 7, 9, 15, 0, 2, 13, 8, 6, -2, 4 (a) Mean= Mode= median= (b) Variance= Standard deviation= (c) Range= IQR(Interquartilerange)= (d) Mid-Range= Mid-Hinge=

Answer 1

Solution:

Given that

x	x2
7	49
-5	25
-8	64
7	49
9	81
0	0
2	4
13	169
8	64
6	36
-2	4
4	16
x = 56	x2 = 786

a ) The sample mean is

Mean    = x/ n

= (7+-5 -8+7+ 9+15+ 0+2+13+ 8+ 6 -2+ 4 / 13 )

= 56 / 13

= 4.3077

The sample mean is = 4.3077

Mode :
In the given data, the observation 7 occurs maximum number of times (2)

∴ Z = 7

Mode = 7

Median :
Observations in the ascending order are :
-8,-5,-2,0,2,4,6,7,7,8,9,13,15

M = Value of ( n + 1 / 2 )^th Observations

= Value of ( 13 + 1 / 2 )^th Observations

   = Value of 7^th Observations

= 6

Median = 6

b ) The Sample Variance is S²

S² =  ( x² ) - (( x )² / n ) / 1 -n )

=  (786 (56 )² / 13 ) / 12

   =  (786 - 541.2308 / 12 )

= (544.7692 / 12 )

=  45.3974

The Sample Variance is S²  =  45.3974

The sample standard is S

S =   Sample Variance

= 45.3974

= 6.7378

The sample standard is S = 6.7378

C ) Range

Observations in the ascending order are :
-8,-5,-2,0,2,4,6,7,7,8,9,13,15

Range = maximum(xi) - minimum(xi

= 15 - 8

= 23

Range = 23.

IQR ( Inter quartilerange )

IQR= Upper quartile X_U - Lower quartile X_L
= - 1 - 8.5

= 9.5

IQR ( Inter quartilerange ) = 9.5

(d) Mid-Range

Observations in the ascending order are :
-8,-5,-2,0,2,4,6,7,7,8,9,13,15

M = midrange
max = maximum value
min = minimum value

M = (max + min) / 2

M =  (maximum value - minimum value / 2)

= (15 - 8 / 2 )

= 3.5

Mid-Range = 3.5

Mid-Hinge

Mid-Hinge = ( Q_{1 +} Q₃  / 2 )

= (- 1 + 8.5 / 2 )

= ​​​​​​​3.75

Mid-Hinge = 3.75