Question

a florist records the amount of money he spent on gasoline each week to deliver orders. the list shows the data for 16 weeks: 32, 38, 40, 44, 44, 46, 49, 53, 55, 58, 62, 65, 68, 70, 72, 81 he put the data in a stem-and-leaf plot. what number did he leave out of the stem-and-leaf plot?
stem | leaf
3 | 2 8
4 | 0 4 6 9
5 | 3 5 8
6 | 2 5 8
7 | 0 2
8 | 1
key: 8 | 1 = 81
options: 32, 65, 44, 81

Explanation:

Step1: Count data in stem - leaf

First, we count the number of data points in the stem - leaf plot. For stem 3: 2 data points (32, 38); stem 4: 4 data points (40, 44, 46, 49)? Wait, no, wait. Wait the original data is 32, 38, 40, 44, 44, 46, 49, 53, 55, 58, 62, 65, 68, 70, 72, 81. Let's list the data from the stem - leaf:

Stem 3: 32, 38 (2 values)

Stem 4: 40, 44, 46, 49? Wait no, the leaves for stem 4 are 0, 4, 6, 9. So the numbers are 40, 44, 46, 49 (4 values)

Stem 5: leaves 3, 5, 8 → 53, 55, 58 (3 values)

Stem 6: leaves 2, 5, 8 → 62, 65, 68 (3 values)

Stem 7: leaves 0, 2 → 70, 72 (2 values)

Stem 8: leaf 1 → 81 (1 value)

Now sum the counts: 2 + 4+3 + 3+2 + 1=15. But the original data has 16 values. So we are missing one value.

Step2: Check original data

Original data: 32, 38, 40, 44, 44, 46, 49, 53, 55, 58, 62, 65, 68, 70, 72, 81.

Now check which value is not in the stem - leaf. Let's list the data from stem - leaf:

From stem 3: 32, 38

Stem 4: 40, 44, 46, 49 (wait, original data has two 44s. In the stem - leaf for stem 4, leaf 4 appears once. So the second 44 is missing. Let's verify:

Original data has two 44s. In the stem - leaf plot, for stem 4, leaf 4 is present once (so 44 is there once), but the original data has two 44s. So the missing number is 44.

Let's check other options:

• 32: present in stem 3 (leaf 2)
• 65: present in stem 6 (leaf 5)
• 81: present in stem 8 (leaf 1)
• 44: in original data, two 44s. In stem - leaf, stem 4 has leaf 4 once, so one 44 is missing.

Answer:

44 (the option with 44)