the image shows a line graph starting from 0 to 10

on the line graph zero has four dots
number one on the line graph shows five dots
number 2 on the line graph shows three dots
number 3 on the line graph shows four dots
number 4 on the line graph shows two dots
number 5 on the line graph shows 0 dots
number 6 on the line graph shows 1 dots
number 7 on the line graph shows 2 dots
numbers 8 and 9 on the line graph shows 0 dots
number 10 on the line graph shows 1 dots

You are trying to find the average number of siblings that your classmates have. In 1 sentences, explain whether the distribution of the data you gathered is symmetrical or skewed and if the mean or median would be the most appropriate center. Also calculate and state the mean and median in your response. Finally, state the best measure of center for the number of siblings.

1 answer

The distribution of the data is skewed to the right, as there are more values concentrated at the lower end (0-4 siblings), while the higher values (5 or more siblings) have significantly fewer occurrences; therefore, the median is the most appropriate measure of center.

To calculate the mean:

\[ \text{Mean} = \frac{(0 \times 4) + (1 \times 5) + (2 \times 3) + (3 \times 4) + (4 \times 2) + (5 \times 0) + (6 \times 1) + (7 \times 2) + (8 \times 0) + (9 \times 0) + (10 \times 1)}{(4 + 5 + 3 + 4 + 2 + 0 + 1 + 2 + 0 + 0 + 1)} \]

\[ = \frac{(0) + (5) + (6) + (9) + (8) + (0) + (6) + (14) + (0) + (0) + (10)}{(22)} \]

\[ = \frac{58}{22} \approx 2.64 \]

Calculating the median:

When we list the data based on occurrences:

  • 0 (4 times),
  • 1 (5 times),
  • 2 (3 times),
  • 3 (4 times),
  • 4 (2 times),
  • 6 (1 time),
  • 7 (2 times),
  • 10 (1 time)

The total is 22 data points, and the median will be the average of the 11th and 12th values, which are both '2' and '3'. So:

\[ \text{Median} = \frac{2 + 3}{2} = 2.5 \]

Thus, the mean is approximately 2.64, the median is 2.5, and the best measure of center for the number of siblings is the median due to the skewed distribution.