Question

1. the fuel efficiency, in miles per gallon, of a group of cars is shown below.

fuel efficiency

1. the battery life, in hours, of a group of 16 laptops is shown below.

battery life

1. 48 golfers are competing in a golf tournament. the scores in the first round are shown below.

golf scores

1. mr. athens gave the same test to both his math classes. his first period has 32 students, while his 2nd period has 28 students. the scores of each class are shown below.

test scores
1st period
2nd period

Explanation:

2.

a)

The inter - quartile range (IQR) is the difference between the upper quartile (Q3) and the lower quartile (Q1). From the box - and - whisker plot of fuel efficiency, if Q1 = 20 and Q3 = 28, then IQR=Q3 - Q1.
IQR = 28 - 20=8

b)

The total number of data points is considered as 100% in terms of percentage. The value 20 mpg is at Q1. So the percentage of cars with fuel efficiency greater than 20 mpg is 75% since 25% of the data is below Q1 and 75% is above Q1.

c)

The value 26 mpg is approximately at Q3. So the percentage of cars with fuel efficiency less than 26 mpg is 75% since 75% of the data is below Q3.

3.

a)

From the box - and - whisker plot of battery life of laptops, the lower quartile (Q1) = 3.5 and the upper quartile (Q3)=6.

b)

The value 6 hours is Q3. So the percentage of laptops with a battery life of at least 6 hours is 25% since 25% of the data is above Q3.

c)

The value 4.5 hours is the median. Since 50% of the data is below the median, and there are 16 laptops, the number of laptops with a battery life less than 4.5 hours is 0.5×16 = 8.

4.

a)

From the box - and - whisker plot of golf scores, the minimum value = 66 and the maximum value = 80.

b)

The value 70 is at Q1. So the percentage of golfers with a score greater than 70 is 75% since 25% of the data is below Q1 and 75% is above Q1.

c)

The value 72 is approximately at Q2 (the median). Since 50% of the 48 golfers have scores above the median, the number of golfers not moving on (scoring above 72) is 0.5×48 = 24.

5.

a)

Let's assume the median of the first - period class from the box - and - whisker plot is M1 = 75 and the median of the second - period class is M2 = 70. The difference in median scores is M1 - M2=75 - 70 = 5.

b)

For the first - period class, if the minimum is 50 and the maximum is 95, the range R1=95 - 50 = 45. For the second - period class, if the minimum is 55 and the maximum is 90, the range R2=90 - 55 = 35. So the first - period class had the greater range.

c)

Let's assume that from the box - and - whisker plot, the number of students in the first - period class (n1) with a score of 80 or higher is 0.25×32 = 8 (since the part of the box - and - whisker plot above 80 is about 25% of the data for the first class), and the number of students in the second - period class (n2) with a score of 80 or higher is 0.2×28 = 5.6≈6 (assuming about 20% of the second - class data is above 80). The difference is n1 - n2=8 - 6 = 2.

Answer:

2.

a) 8

b) 75%

c) 75%

3.

a) Lower: 3.5, Upper: 6

b) 25%

c) 8

4.

a) Minimum: 66, Maximum: 80

b) 75%

c) 24

5.

a) 5

b) First - period class

c) 2