Question

home sales prices (hundred thousands) (ten thousands) 0 667778999 1 02447778889999 2 0011234445667889 3 00011227 the stem-and-leaf plot above shows house sale prices over the last week in tacoma. what was the most expensive house sold? give your answer in dollars $

Explanation:

Step1: Identify the stem and leaf structure

The stem represents the hundred thousands place, and the leaf represents the ten thousands place. To find the most expensive house, we need the largest stem and the largest leaf within that stem.

Step2: Find the largest stem

Looking at the stems (0, 1, 2, 3), the largest stem is 3.

Step3: Find the largest leaf in stem 3

The leaves for stem 3 are 0, 0, 0, 1, 1, 2, 2, 7. The largest leaf here is 7.

Step4: Calculate the price

The stem is 3 (hundred thousands place), so that's \(3\times100000 = 300000\). The leaf is 7 (ten thousands place), so that's \(7\times10000 = 70000\). Adding these together: \(300000 + 70000 = 370000\). Wait, no, wait. Wait, the stem is hundred thousands, leaf is ten thousands? Wait, no, let's re - check. Wait, the stem is (hundred thousands), so the stem value is \(stem\times100000\), and the leaf is a digit that represents ten thousands? Wait, no, actually, in a stem - and - leaf plot, the stem is the leading digit(s) and the leaf is the trailing digit(s). Wait, the first column is (hundred thousands), so the stem is the number of hundred thousands, and the leaf is the number of ten thousands? Wait, no, let's think about place values. Let's take an example. For stem 0, leaf 6: the number would be \(0\times100000+6\times10000 = 60000\)? Wait, no, maybe the stem is the hundreds of thousands place, and the leaf is the ten thousands, thousands, etc.? Wait, no, the problem says (hundred thousands) and (ten thousands). Wait, the leaf is a single digit? Wait, no, looking at the leaves: for stem 0, the leaf is 667778999 – that's multiple digits. Oh! Wait, I misinterpreted. The stem is the number of hundred thousands, and the leaf is a number in ten thousands (i.e., the leaf is a number where each digit is in the ten thousands, thousands, hundreds, tens, ones? Wait, no, the label is (hundred thousands) and (ten thousands). Wait, maybe the stem is the hundreds of thousands digit, and the leaf is the ten thousands digit? But the leaves are multiple digits. Wait, no, let's look at the stem - and - leaf plot structure. In a stem - and - leaf plot, the stem is on the left, and the leaf is on the right, with each leaf digit representing a data point. Wait, the problem says "Home Sales Prices" with (hundred thousands) as stem and (ten thousands) as leaf. Wait, maybe the stem is the number of hundred thousands, and the leaf is a number where each digit is the ten thousands place? No, that doesn't make sense. Wait, let's take stem 3, leaf 00011227. The largest leaf digit here is 7. Wait, no, maybe the stem is the hundreds of thousands, and the leaf is the ten thousands, so the number is \(stem\times100000+leaf\times10000\). Wait, but the leaf is a number, not a digit. Wait, no, looking at the leaves: for stem 0, the leaf is 667778999 – that's 9 digits. Wait, maybe the stem is the hundreds of thousands, and the leaf is the number in ten thousands (i.e., the leaf is a number where the first digit is ten thousands, second is thousands, etc.). Wait, no, let's think of the stem as the coefficient for \(10^5\) (hundred thousands) and the leaf as a number that is added, where the leaf's digits are in \(10^4\) (ten thousands), \(10^3\) (thousands), etc. So for stem 3, the leaf is 00011227. The largest number in the leaf for stem 3 is 7 (the last digit). Wait, no, the leaf is a number, so we need to take the largest number in the leaf for the largest stem. The largest stem is 3. The leaf for stem 3 is 00011227. Let's parse the leaf: the digits are 0, 0, 0, 1, 1, 2, 2, 7. Wait, no, maybe the leaf is a sequence of digits, each representing a data point's ten - thousands place? No, that can't be. Wait, maybe the stem is the hundreds of thousands, and the leaf is the number in ten thousands (i.e., the leaf is a number where the value is \(leaf\times10000\)). Wait, no, let's take an example from stem 0: leaf is 667778999. If stem is 0 (hundred thousands), then the numbers would be \(0\times100000 + 6\times10000=60000\), \(0\times100000 + 6\times10000 = 60000\), \(0\times100000+7\times10000 = 70000\), etc. But that would mean multiple data points. But we need the maximum. So the maximum stem is 3. Then, within stem 3, the maximum leaf digit (since each leaf digit is a ten - thousands place? No, wait, maybe the leaf is a number, and we need to take the largest number in the leaf for stem 3. The leaf for stem 3 is 00011227. Let's consider the leaf as a number: 00011227 is 11227? No, leading zeros don't matter. Wait, 00011227 is 11227? No, 00011227 is 11227? Wait, no, 00011227 is 11227 (since leading zeros are not significant). Wait, no, maybe the leaf is a number where each digit is a separate data point. Wait, the stem - and - leaf plot: stem 0 has leaves 6,6,7,7,7,8,9,9,9 (wait, 667778999 has 9 digits, so 9 data points: 6,6,7,7,7,8,9,9,9). Stem 1 has leaves 0,2,4,4,7,7,7,8,8,8,9,9,9,9 (14 digits). Stem 2 has leaves 0,0,1,1,2,3,4,4,4,5,6,6,7,8,8,9 (16 digits). Stem 3 has leaves 0,0,0,1,1,2,2,7 (8 digits). Ah! I see, I misread the leaves. Each digit in the leaf column is a separate data point. So for stem 0, the leaves are 6,6,7,7,7,8,9,9,9 (each digit is a leaf, representing the ten - thousands place? Wait, no, the stem is (hundred thousands), so the number is \(stem\times100000+leaf\times10000\)? Wait, no, let's think of the place values. The stem is the hundreds of thousands digit, and the leaf is the ten thousands digit? No, because if stem is 3 (hundred thousands), and leaf is 7 (ten thousands), then the number is \(3\times100000 + 7\times10000=300000 + 70000 = 370000\)? Wait, no, that can't be, because the leaf for stem 3 is 7, but let's check the stem 2. Wait, no, let's re - express the stem - and - leaf plot correctly. In a stem - and - leaf plot, the stem is the leading part, and the leaf is the trailing part. So if the stem is (hundred thousands), then the stem value is \(stem\times100000\), and the leaf is a number that is added, where the leaf's digits are in the ten thousands, thousands, hundreds, tens, and ones? Wait, no, the problem says "Give your answer in dollars" and the stem is (hundred thousands) and leaf is (ten thousands). Wait, maybe the stem is the number of hundred thousands, and the leaf is the number of ten thousands, so the total price is \(stem\times100000+leaf\times10000\). But the leaf is a digit? No, the leaves are multiple digits. Wait, I think I made a mistake earlier. Let's look at the stem 3: the leaf is 00011227. The largest digit in the leaf for stem 3 is 7. So the stem is 3 (hundred thousands), so \(3\times100000 = 300000\), and the leaf is 7 (ten thousands), so \(7\times10000 = 70000\). Wait, but that would be 370000. But wait, let's check stem 2. The largest leaf digit in stem 2 is 9. So stem 2: \(2\times100000=200000\), leaf 9: \(9\times10000 = 90000\), total 290000. Stem 3: \(3\times100000 = 300000\), leaf 7: \(7\times10000=70000\), total 370000. Wait, but is the leaf a single digit? Wait, the leaf column has numbers like 667778999 for stem 0 – that's 9 digits, so 9 data points, each with stem 0 and leaf digit (6,6,7,7,7,8,9,9,9). So each leaf digit is a separate data point. So for stem 3, the leaf digits are 0,0,0,1,1,2,2,7. So the data points for stem 3 are: \(3\times100000+0\times10000 = 300000\), \(3\times100000+0\times10000 = 300000\), \(3\times100000+0\times10000 = 300000\), \(3\times100000+1\times10000 = 310000\), \(3\times100000+1\times10000 = 310000\), \(3\times100000+2\times10000 = 320000\), \(3\times100000+2\times10000 = 320000\), \(3\times100000+7\times10000 = 370000\). Ah! Now I see. Each digit in the leaf column is a separate leaf, representing the ten - thousands place. So the number is \(stem\times100000+leaf\times10000\). So for stem 3, the largest leaf digit is 7, so the number is \(3\times100000 + 7\times10000=300000 + 70000 = 370000\). Wait, but let's confirm with stem 2. The largest leaf digit in stem 2 is 9, so the number would be \(2\times100000+9\times10000 = 200000+90000 = 290000\), which is less than 370000. Stem 1: largest leaf digit is 9, number is \(1\times100000+9\times10000 = 190000\). Stem 0: largest leaf digit is 9, number is \(0\times100000+9\times10000 = 90000\). So the largest number is 370000.

Answer:

370000