Question

1 select all the distribution shapes for which it is most often appropriate to use the mean. a bell - shaped b bimodal c skewed d symmetric e uniform
2 for which distribution shape is it usually appropriate to use the median when summarizing the data? a bell - shaped b skewed c symmetric 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.

Explanation:

Step1: Recall when to use mean

The mean is most appropriate for symmetric distributions. Bell - shaped and uniform distributions are symmetric, and symmetric distributions in general work well with the mean. Bimodal and skewed distributions are not ideal for the mean.

Step2: Recall when to use median

The median is a better measure for skewed distributions as the mean can be pulled in the direction of the skew. Bell - shaped, symmetric and uniform distributions are better summarized by the mean in most cases.

Step3: Analyze dot - plot

Count the number of data points in the dot - plot. There are 1 + 1+1+1 + 3+4+2+1=14 data points. The median is the average of the 7th and 8th ordered data points. The ordered data: 5,6,7,8,9,9,9,10,10,10,10,11,11,12. The 7th value is 9 and the 8th is 10, so the median is $\frac{9 + 10}{2}=9.5$. The mean $\bar{x}=\frac{5\times1+6\times1+7\times1+8\times1+9\times3+10\times4+11\times2+12\times1}{14}=\frac{5 + 6+7+8+27+40+22+12}{14}=\frac{127}{14}\approx9.07$. The median is greater. The distribution is slightly skewed left (tail on the left side), and in a left - skewed distribution, the median is typically greater than the mean.

Answer:

1. A. bell - shaped, D. symmetric, E. uniform
2. B. skewed
3. The median is greater. The distribution is slightly left - skewed. In a left - skewed distribution, the median is typically greater than the mean.