Question

Round to 4th decimal place, if needed. Use your calculator to find the 5-number summary of the dataset: 143,15,7,47,3,48,40,18,45,49) What is the Q1? 2. What is the Median? 3.What is the Q3? 4. What is the IQR?

Answer 1

Solution:

Given that,

Arranging Observations in the ascending order,
3,7,15,18,40,43,45,47,48,49

n = 10

1 ) Q₁

Q₁ = ( n + 1 / 4 )^th value of the observation

= ( 10 + 1 / 4 )^th value of the observation

= ( 11 / 4 )^th value of the observation

= 2.75^th value of the observation

= 2 ^nd Observation +0.75 ( 3^rd + 2 ^nd )

= 7 + 0.75 ( 16 - 7 )

= 7 + 0.75( 8 )

= 7 + 6

= 13

Q₁ = 13

2 ) Median

M = ( n / 2 )^th value of the observation + ( n /2 + 1 )^th value of the observation ) / 2

= (10 / 2 )^th value of the observation + ( 10 /2 + 1 )^th value of the observation ) / 2

= (5 )^th value of the observation + ( 6 )^th value of the observation ) / 2

= 2.75^th value of the observation

= 40 + 43 / 2

= 83 /2

= 41 .5

Median = 41.5

1 ) Q₃

Q₃= ( 3*n + 1 / 4 )^th value of the observation

= ( 3 * 11 / 4 )^th value of the observation

= ( 33 / 4 )^th value of the observation

= 8.25^th value of the observation

= 8^th Observation +0.25 ( 9^th + 8^th )

= 47 + 0.25 ( 48 - 47 )

= 47 + 0.25( 1 )

= 47 + 0.25

= 47.25

Q₃ = 47.25

4 ) Inter Quartile range is IQR

IQR = Q_{3 -} Q₁

= Upper Quartile - Lower Quartile

= 47.25 - 13

= 34.25

IQR = 34.25