# Question 355ed

Sep 23, 2017

(a) See explanation.

(b) $\frac{27}{60}$

(c) $0.1$

#### Explanation:

(a) Construct a stem-and-leaf plot for the data.

The column of 0's, 1's, ... 5's you are given is the stem of your stem-and-leaf plot. These digits stand for the ones place digits of the data set. The leaves of the plot will be the tenths place digits.

The stem-and-leaf plot gets filled in like this: for each measurement, we add a leaf into the plot at its matching stem.

Side note: since the stem of this plot has two of each digit (0 through 5), that means the first of each digit will get the leaves 0 1 2 3 4, and the second will get the leaves 5 6 7 8 9.

Example: the first measurement is $1.2$. Since the ones digit is a 1 and the tenths place is a low digit (2), the stem for this value is the first 1. To add this value to the plot, type a '2' in the textbox beside the first '1'.

Working down, the next measurement is $0.1$. The ones digit is a 0 and the tenths place is a low digit (1), so the stem for 0.1 is the first 0. Type a '1' in the textbox next to the first 0.

Keep doing this for all the measurements. When a leaf textbox already has one (or more) leaf digits in it, new leaves can be added, sorted in increasing order. Example: the 3rd measurement is $1.2$, so it will share the same leaf textbox as the $1.2$ from above. Add a '2' to the first '1' textbox next to the '2' already there, with a space in between them.

After you've added all the measurements to the plot, the rows starting with 0 should look like this:

$0 \text{ | 1 2 3 4 4 4}$
$0 \text{ | 5 5 5 6 6 6 6 7 7 7 8 8 8 8 9 9 9}$

I'll leave the other rows for you to fill in. (If a row has no leaves in it, remember to fill that textbox with 'NONE'.)

(b) What fraction of the service times are less than or equal to one minute?

This is calculated by simply counting the number of leaves in the two 0 rows, and the number of 0's in the first '1' stem. Add these counts together, then divide by the total number of measurements given (which is 60):

([("number of leaves"), ("in both 0 stems")] + [("number of 0's"), ("in the first 1 stem")])/(["total number of measurements"])#

$= \frac{23 + 4}{60}$

$= \frac{27}{60}$

The fraction is $\frac{27}{60}$.

(c) What is the smallest of the 60 measurements?

The first entry in the top textbox represents your smallest measurement. In this case, that will be the '1' in the first 0 stem. Thus, the smallest measurement in the set is $0.1$.