Statistics on SAT Math: Strategies for Mean, Median, Mode - Free Printable

We are given a survey of students from Lincoln School and Washington School, where 300 students were randomly selected from each school. The table shows how many students from each school reported having 0, 1, 2, 3, or 4 siblings.

We are asked to find the median number of siblings for all the students surveyed (i.e., the 600 students: 300 from Lincoln + 300 from Washington).

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Step 1: Understand what the median is

The median is the middle value when all values are arranged in order.

Since we have 600 students, the median will be the average of the 300th and 301st values when sorted by number of siblings.

So, we need to determine how many students have 0, 1, 2, etc. siblings in total across both schools, then find which sibling count includes the 300th and 301st students.

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Step 2: Combine the data from both schools

Let’s add up the number of students from both schools for each number of siblings:

| Number of Siblings | Lincoln | Washington | Total |
|--------------------|---------|------------|-------|
| 0 | 120 | 140 | 260 |
| 1 | 80 | 110 | 190 |
| 2 | 60 | 30 | 90 |
| 3 | 30 | 10 | 40 |
| 4 | 10 | 10 | 20 |
| Total | 300 | 300 | 600 |

Now, let’s compute cumulative totals to find where the 300th and 301st students fall.

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Step 3: Cumulative frequency

| Siblings | Frequency | Cumulative Frequency |
|----------|-----------|----------------------|
| 0 | 260 | 260 |
| 1 | 190 | 260 + 190 = 450 |
| 2 | 90 | 450 + 90 = 540 |
| 3 | 40 | 540 + 40 = 580 |
| 4 | 20 | 580 + 20 = 600 |

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Step 4: Find the median

We want the 300th and 301st students in the ordered list.

- The first 260 students have 0 siblings.
- The next 190 students (from 261 to 450) have 1 sibling.

So:
- The 261st to 450th students have 1 sibling.

Therefore:
- The 300th student has 1 sibling
- The 301st student also has 1 sibling

So the median is the average of the 300th and 301st values:

$$
\text{Median} = \frac{1 + 1}{2} = 1
$$

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✔ Final Answer: B) 1

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> Note: The total number of students at each school (2,400 and 3,300) is not needed here because we're only analyzing the surveyed sample of 300 from each school. The question asks about the students surveyed, not the entire population.

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✔️ Answer: B) 1