To analyze the distribution of the data on siblings, we first note that the data points (number of siblings) and their frequencies suggest a right-skewed distribution. There are more students with fewer siblings (0 to 3), with the frequencies decreasing as the number of siblings increases, which is characteristic of skewed data.
To calculate the mean, we first find the total number of siblings:
- Total siblings = (0 * 4) + (1 * 5) + (2 * 3) + (4 * 4) + (5 * 0) + (6 * 1) + (7 * 2) + (8 * 0) + (9 * 0) + (10 * 1) = 0 + 5 + 6 + 16 + 0 + 6 + 14 + 0 + 0 + 10 = 57 siblings.
Next, the total number of students is
- Total students = 4 + 5 + 3 + 4 + 0 + 1 + 2 + 0 + 0 + 1 = 20.
Thus, the mean is:
- Mean = Total siblings / Total students = 57 / 20 = 2.85.
To find the median, we list out the siblings according to their frequency:
- 0, 0, 0, 0 (4)
- 1, 1, 1, 1, 1 (5)
- 2, 2, 2 (3)
- 4, 4, 4, 4 (4)
- 6 (1)
- 7, 7 (2)
- 10 (1)
Listing:
0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 4, 4, 4, 4, 6, 7, 7, 10
The median is the average of the 10th and 11th values, which are 2 and 2, so:
- Median = (2 + 2) / 2 = 2.
In this case, the median is the most appropriate measure of center due to the right-skewed distribution, which can disproportionately affect the mean. The median, being less sensitive to extreme values, provides a better indication of the "typical" number of siblings.
In conclusion, the mean is 2.85, the median is 2, and the best measure of center for the number of siblings is the median.