Final answer:
To find the upper quartile given that the coefficient of quartile deviation is 0.50 and the lower quartile is 20, we set up an equation and solve for the upper quartile (Q3). The calculation shows that the upper quartile (Q3) is 60.
Step-by-step explanation:
The coefficient of quartile deviation is a measure that indicates how spread out the middle 50% of values are in a data set. It is calculated by dividing the difference between the third quartile (Q3) and first quartile (Q1) by the sum of Q3 and Q1. Given that the coefficient of quartile deviation is 0.50 and the lower quartile (Q1) is 20, we can set up an equation to find the upper quartile (Q3).
The formula for the coefficient of quartile deviation is: (Q3 - Q1) / (Q3 + Q1) = coefficient of quartile deviation
Plugging in our known values gives: (Q3 - 20) / (Q3 + 20) = 0.50
To solve for Q3, we multiply both sides by the denominator (Q3 + 20) to eliminate the fraction: Q3 - 20 = 0.50 × (Q3 + 20)
Expanding the right side and rearranging terms leads to: Q3 - 20 = 0.50Q3 + 10
This simplifies to: 0.50Q3 - 20 = 10
Adding 20 to both sides gives: 0.50Q3 = 30
Finally, dividing both sides by 0.50 gives the value of the upper quartile:
Q3 = 60