Question

key: 1|10 represents 10 minutes
what is the median number of minutes the second graders spent reading?
0 | 9
1 | 0 5 8
2 | 0 0 2 5 5 9
3 | 0 2 2 2 4 5 6 7
4 | 1 3 5

Explanation:

Step1: Interpret the stem-and-leaf plot

The key is "1|10 represents 10 minutes", so the first digit is the tens place and the second (and subsequent) digits are the ones place. Let's list all the data points:

• For row 0: 9 (so 9 minutes)
• For row 1: 10, 15, 18 (wait, no, the stem is 1, so the leaves are 0,5,8? Wait, the stem-and-leaf plot has stems 0,1,2,3,4. Let's parse each stem:
• Stem 0: leaf 9 → 09 = 9 minutes
• Stem 1: leaves 0,5,8 → 10, 15, 18 minutes
• Stem 2: leaves 0,0,2,5,5,9 → 20, 20, 22, 25, 25, 29 minutes
• Stem 3: leaves 0,0,2,2,2,4,5,6,7 → 30, 30, 32, 32, 32, 34, 35, 36, 37 minutes
• Stem 4: leaves 1,3,5 → 41, 43, 45 minutes

Now let's count the number of data points:

• Stem 0: 1
• Stem 1: 3 (total so far: 1 + 3 = 4)
• Stem 2: 6 (total so far: 4 + 6 = 10)
• Stem 3: 9 (total so far: 10 + 9 = 19)
• Stem 4: 3 (total: 19 + 3 = 22)

So there are 22 data points. The median for an even number of data points is the average of the \(\frac{n}{2}\)-th and \((\frac{n}{2}+1)\)-th values when sorted. Here, \(n = 22\), so \(\frac{n}{2}=11\) and \(\frac{n}{2}+1 = 12\). We need the 11th and 12th values.

Let's list the data in order:
9, 10, 15, 18, 20, 20, 22, 25, 25, 29, 30, 30, 32, 32, 32, 34, 35, 36, 37, 41, 43, 45

Wait, let's count the positions:
1: 9
2: 10
3: 15
4: 18
5: 20
6: 20
7: 22
8: 25
9: 25
10: 29
11: 30
12: 30

Ah, so the 11th value is 30 and the 12th value is 30.

Step2: Calculate the median

The median is the average of the 11th and 12th values. Since both are 30, the average is \(\frac{30 + 30}{2}=30\).

Answer:

30