4 5 3 4 2 0 1 2 0 0 1

Question

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You are trying to find the average number of siblings that your classmates have. In 3–5 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.

Answer 1

To analyze the distribution of the number of siblings your classmates have, we should first calculate the mean and median.

1. Mean Calculation:

   • Total number of siblings: \(4 + 5 + 3 + 4 + 2 + 0 + 1 + 2 + 0 + 0 + 1 = 22\)
   • Total number of classmates: \(11\)
   • Mean = \( \frac{22}{11} = 2\)

2. Median Calculation:

   • Arranging the data: \(0, 0, 0, 1, 1, 2, 2, 3, 4, 4, 5\)
   • The median is the middle value. For \(11\) data points, the median will be the \(6^{th}\) value, which is \(2\).

The calculated mean and median both equal \(2\). However, the distribution appears to be slightly skewed to the right, as the majority of the data points cluster towards the lower end with a few higher values (specifically, \(4\) and \(5\)). In this case, although the mean and median are the same, the median is often preferred as a measure of center in skewed distributions because it is less affected by outliers. Therefore, the best measure of center for the number of siblings is the median, which is \(2\).