Question

1, select all the distribution shapes for which it is most often appropriate to use the mean, a bell - shaped d symmetric b bimodal e uniform c skewed 2, for which distribution shape is it usually appropriate to use the median when summarizing the data? a bell - shaped c symmetric b skewed d uniform 3, the number of writing instruments in some teachers desks is displayed in the dot plot. which is greater, the mean or the median? explain your reasoning using the shape of the distribution. 4, a student has these scores on their assignments. the teacher is considering dropping a lowest score. what effect does eliminating the lowest value, 0, from the data set have on the mean and median? (lesson 1 - 9) 0, 40, 60, 70, 75, 80, 85, 95, 95, 100

Explanation:

1.

The mean is most appropriate for distributions that are symmetric. Bell - shaped distributions are a type of symmetric distribution (normal distribution is bell - shaped and symmetric). Uniform distributions are also symmetric (all values have equal frequency). Bimodal distributions (two peaks) can be symmetric or not, but in general, the mean is still a good measure for symmetric bimodal distributions. Skewed distributions are better described by the median.

The median is less affected by extreme values. In skewed distributions, there are extreme values (either on the left or right tail). Bell - shaped, symmetric, and uniform distributions are not affected as much by extreme values (in bell - shaped and symmetric, the mean and median are close; in uniform, all values are evenly distributed).

Looking at the dot - plot, the distribution is slightly skewed to the right (more data on the left side). In a right - skewed distribution, the mean is greater than the median. The mean is pulled in the direction of the skew (right in this case) because it is affected by the larger values on the right side, while the median is the middle value and is less affected by the extreme values.

Answer:

A. bell - shaped, D. symmetric, E. uniform

2.