Question

legend asks the students in his class, \how many minutes does it take you to get to school?\ the histogram shows the data. which statement best describes the distribution? the distribution is skewed right. the distribution is skewed left. the distribution is symmetric. the distribution has an outlier.

Explanation:

A skewed - left distribution has a longer tail on the left side. In a histogram, if the left side (lower values) has a longer tail compared to the right side, it is skewed left. Looking at the given histogram, the left - hand side (lower time values) has a shorter bar but when considering the "tail" (the spread of data), the left side has fewer data points but the right side (higher time values) has a more abrupt stop. Wait, no. Wait, actually, in a skewed - left distribution, the mean is less than the median. Visually, if we imagine the "hump" of the histogram (the tallest bar is around 6 - 9 minutes). The left side (0 - 3 minutes) has a shorter bar, but if we consider the "tail" (the spread of data from the peak to the left and right). The left side (towards 0) has a shorter "tail" (fewer data points in the lower intervals) and the right side (towards 12) also has a shorter "tail". Wait, no. Wait, actually, for a skewed - left distribution, the tail is on the left. But looking at the histogram, the left side (0 - 3) has a bar height of 1 (approx), 3 - 6 has 4, 6 - 9 has 10, 9 - 12 has 4, 12 - 15 has 1. If we fold the histogram along a vertical line, the left side (0 - 6) has a total frequency of \(1 + 4=5\) and the right side (9 - 15) has a total frequency of \(4 + 1 = 5\). But the peak is at 6 - 9. The "tail" on the left (from 6 to 0) is shorter in terms of bar - height decrease (from 10 to 4 to 1) and on the right (from 10 to 4 to 1). Wait, no. Wait, actually, in a skewed - left distribution, the tail is on the left. But if we look at the shape, the left side (lower values) has a shorter "tail" (fewer data points in the lower intervals) compared to a normal distribution. Wait, no. Wait, actually, if we consider the definition: A distribution is skewed left if the left tail (smaller values) is longer. But in our case, the frequencies on the left (0 - 3: 1, 3 - 6: 4) and on the right (9 - 12: 4, 12 - 15: 1). The left side (when moving from the peak at 6 - 9 to 0) has a "tail" that decreases (10 to 4 to 1) and the right side (from 10 to 4 to 1). But if we consider the position of the peak. Wait, no. Wait, another approach: A symmetric distribution would have the left half (mirror - image) equal to the right half. Here, if we consider the intervals 0 - 3 and 12 - 15 (both frequency 1), 3 - 6 and 9 - 12 (both frequency 4), and 6 - 9 (frequency 10). If we fold the histogram along the line \(x = 7.5\) (mid - point of 6 - 9 interval), the left side (0 - 6) and right side (9 - 15) are mirror images. So the distribution is symmetric.

Answer:

The distribution is symmetric.