# Question #355ed

##### 1 Answer

(a) See explanation.

(b)

(c)

#### 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 *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

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

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

#0" | 1 2 3 4 4 4"#

#0" | 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"])#

#=(23+4)/60#

#=27/60#

The fraction is

**(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