Question

charles owns a catering business. the amount his 10 most recent clients spent is shown in the histogram below.
cost per event
why is the graph misleading?
○ the x - axis scale shows the data is more clustered than it actually is.
○ the y - axis scale shows the data is more skewed than it actually is.
○ the scales are different on the x - axis and the y - axis

Explanation:

To determine why the histogram is misleading, we analyze the x - axis intervals. The x - axis has intervals: 1000 - 1499, 1500 - 1999, 2000 - 2499, 3000 - 3499. The first three intervals have a width of 500 (1499 - 1000 = 499≈500, 1999 - 1500 = 499≈500, 2499 - 2000 = 499≈500), but the last interval is 3000 - 3499, which is also 500? Wait, no, wait, 1000 - 1499 is 500, 1500 - 1999 is 500, 2000 - 2499 is 500, but 3000 - 3499: the gap between 2499 and 3000 is 501, which is a large gap. However, the main issue is the x - axis scale. The intervals are set in a way that makes the data look more clustered. For example, the first three intervals are close (1000 - 1499, 1500 - 1999, 2000 - 2499) and then there's a jump to 3000 - 3499. This makes the data appear more clustered together than it actually is because the x - axis scale compresses the space between the lower intervals and then has a gap before the last interval, giving a false sense of how close the data points are. The y - axis is about the number of events, and its scale (0 - 4) doesn't skew the data in terms of skewness of the distribution. The third option is not clear, but the first option says the x - axis scale shows the data is more clustered than it actually is, which matches our analysis.

Answer:

The x - axis scale shows the data is more clustered than it actually is.