Question

Last year, 400 people participated in a model rocket competition in the Mojave Desert. Prizes were awarded to participants whose model rockets reached the highest vertical distances. Below is a boxplot for the vertical distances (in meters) achieved by the model rockets of all 400 participants: Vertical Distances (in meters) 150 200 250 300 350 400 450 Use the boxplot to answer the following: (a) What was the first quartile, median, and third quartile of vertical distances? Q1 Median = Q3 = (b) What was the highest vertical distance achieved?

Answer 1

A.

First quartile Q1 = 230

Median = 250

Third quartile Q3 = 300

(In box plot, the left side of the box gives us the values value of Q1 which is corresponding to 230 on scale. The middle line in th box represents median whuch coresond to value 250 and the right side of Box represents third quartile corresponding to value 300

B.

The highest vertical distance(in meters) achieved is 450.

(the right most point of the horizontal line represents the maximum value which is corresponding to 450 on scale.)

C.

By theory,

P(X < Q3) = 0.75

This means that 75% of the data takes values upto Q3

P(X < Q1) = 0.25

This means that 25% of the data takes values upto Q1

Thus,

75% of the model rockets achieved vertical distances upto Q3 = 300 meters

25% of the model rockets achieved vertical distance upto Q1 = 230 meters

Thus, percent of models that achieved vertical distance between Q1 and Q3

(Let X be the distance achieved by model rocket)

= P(Q1 < X < Q3)

= P(X < Q3) - P(X < Q1)

= 0.75 - 0.25

= 0.50 or 50%

Hence 50 percent of model rockets achieved vertical distance of between 230 and 300 meters