Question

Ella surveys a random sample of 20 seventh graders about the number of siblings they have.


The table shows the results of her survey.
student. A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,R,S
number. 1,1,2,0,2,1,3,1,1,6,1,2,3,2,1,3,2,0,2

Answer 1

To analyze the survey results from Ella's sample of 20 seventh graders regarding the number of siblings they have, let's first summarize the data in a more structured way.

Here’s a breakdown of the survey results:

**Number of Siblings:**
- **0 siblings:** 2 students (D, S)
- **1 sibling:** 8 students (A, B, F, H, I, K, L, O)
- **2 siblings:** 6 students (C, E, M, N, Q, R)
- **3 siblings:** 3 students (G, J, P)
- **6 siblings:** 1 student (Q)

Now, we can create a frequency table to summarize this information:

| Number of Siblings | Frequency |
|---------------------|-----------|
| 0 | 2 |
| 1 | 8 |
| 2 | 6 |
| 3 | 3 |
| 6 | 1 |
| **Total** | **20** |

Next, we can calculate additional statistics such as the mean, median, and mode.

### Mean
To calculate the mean number of siblings:

\[
\text{Mean} = \frac{\text{Total number of siblings}}{\text{Total number of students}}
\]

Calculating the total number of siblings:

\[
(0 \times 2) + (1 \times 8) + (2 \times 6) + (3 \times 3) + (6 \times 1) = 0 + 8 + 12 + 9 + 6 = 35
\]

Thus, the mean is:

\[
\text{Mean} = \frac{35}{20} = 1.75
\]

### Median
To find the median, we need to list the number of siblings in ascending order:

0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 6

With 20 data points (even), the median will be the average of the 10th and 11th values:

10th: 2
11th: 2

\[
\text{Median} = \frac{2 + 2}{2} = 2
\]

### Mode
The mode is the value that appears most frequently. From our frequency table, we see that 1 is the most common number of siblings (8 occurrences), so:

\[
\text{Mode} = 1
\]

### Summary of Results
- **Mean:** 1.75
- **Median:** 2
- **Mode:** 1

This analysis gives us a good overview of the number of siblings among a random sample of seventh graders surveyed by Ella.