Question

the following data are the numbers of miles of bike lanes per square mile for a sample of 10 of the top 25 cities with the most miles of bike lanes. complete parts (a) through (d). a. construct a stemplot. miles of bike lanes 1 5 2 2 6 7 8 9 3 0 7 7 4 3 b. how many of the 10 cities have at most 3.0 miles of bike lanes per square mile? of the 10 cities, 7 have at most 3.0 miles of bike lanes per square mile. (type a whole number.) c. find the proportion of the 10 cities that have at least 3.7 miles of bike lanes per square mile. of the 10 cities, 0.3 have at least 3.7 miles of bike lanes per square mile. (round to one decimal place as needed.) d. find the 80th percentile of the 10 observations. the 80th percentile of the 10 observations is miles of bike lanes per square mile. (type an integer or a decimal. do not round.)

Explanation:

Step1: Arrange data in ascending order

1.5, 2.2, 2.6, 2.7, 2.8, 2.9, 3.0, 3.7, 3.7, 4.3

Step2: Construct stem - plot

Stem | Leaf
---|---
1 | 5
2 | 2 6 7 8 9
3 | 0 7 7
4 | 3

Step3: Count number of values ≤ 3.0

There are 7 values (1.5, 2.2, 2.6, 2.7, 2.8, 2.9, 3.0) that are at most 3.0 miles of bike lanes per square mile.

Step4: Calculate proportion of values ≥ 3.7

There are 3 values (3.7, 3.7, 4.3) that are at least 3.7 miles of bike lanes per square mile. Proportion = $\frac{3}{10}=0.3$

Step5: Calculate 80th percentile

$i = \frac{80}{100}\times n=\frac{80}{100}\times10 = 8$. The 80th percentile is the 8th - ordered value. Since $i$ is an integer, the 80th percentile is the average of the 8th and 9th ordered values. The 8th value is 3.7 and the 9th value is 3.7, so the 80th percentile is 3.7.

Answer:

a. Stem - plot: Stem | Leaf
---|---
1 | 5
2 | 2 6 7 8 9
3 | 0 7 7
4 | 3
b. 7
c. 0.3
d. 3.7