A dot plot is labeled 'Number of Siblings.' The horizontal axis ranges from 0 to 5 by 1-unit increments. The plot has 2 dots above 0, 7 dots above 1, 4 dots above 2, 4 dots above 3, 2 dots above 4, and 1 dot above 5.

Question

Compare the values and calculate the median of the given data.

(1 point)
Responses

4
4

2
2

3
3

1

Answer 1

To find the median of the given data from the dot plot, we first need to compile the data based on the number of dots:

• 0 siblings: 2 dots (2 entries of 0)
• 1 sibling: 7 dots (7 entries of 1)
• 2 siblings: 4 dots (4 entries of 2)
• 3 siblings: 4 dots (4 entries of 3)
• 4 siblings: 2 dots (2 entries of 4)
• 5 siblings: 1 dot (1 entry of 5)

Now, let's list all the entries:

• 0, 0 (2 entries)
• 1, 1, 1, 1, 1, 1, 1 (7 entries)
• 2, 2, 2, 2 (4 entries)
• 3, 3, 3, 3 (4 entries)
• 4, 4 (2 entries)
• 5 (1 entry)

Now we write them out in order:

0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 5

To find the median, we need to determine the middle value.

To do this, we count the total number of entries:

• There are 2 (0s) + 7 (1s) + 4 (2s) + 4 (3s) + 2 (4s) + 1 (5) = 20 entries in total.

Since 20 is an even number, the median will be the average of the 10th and 11th entries in the ordered list.

Counting the entries:

1. 0 (1st)
2. 0 (2nd)
3. 1 (3rd)
4. 1 (4th)
5. 1 (5th)
6. 1 (6th)
7. 1 (7th)
8. 1 (8th)
9. 1 (9th)
10. 2 (10th)
11. 2 (11th)

The 10th and 11th entries both equal 2.

Thus, the median is:

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

So the median of the given data is 2.