Question

for the histogram on the right determine whether the mean is greater than, less than, or approximately equal to the median.
justify your answer.
which of the following is correct?
a. \\( \bar { x } > m \\) because the histogram is skewed right.
b. \\( \bar { x } = m \\) because the histogram is symmetric.
c. \\( \bar { x } < m \\) because the histogram is skewed left.
d. \\( \bar { x } > m \\) because the histogram is skewed left.
e. \\( \bar { x } < m \\) because the histogram is symmetric.
f. \\( \bar { x } = m \\) because the histogram is skewed right.

Explanation:

Step1: Recall the relationship between mean and median for skewed distributions

For a right - skewed distribution, the mean is pulled towards the tail (higher values), so \(\bar{x}>M\). For a left - skewed distribution, the mean is pulled towards the tail (lower values), so \(\bar{x}

Step2: Analyze the given histogram

Looking at the histogram, it is skewed left. In a left - skewed distribution, the tail is on the left side. The mean is affected by the extreme values in the tail. Since the tail is on the left (lower values), the mean is less than the median.

Answer:

C. \(\bar{x}