the table shows the height in stories of several buildings with one value added. the data are presented in…

Explanation:

Step1: Calculate original mean

The original data set is (56,60,64,80,110). The mean formula is (\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}), where (n = 5), (\sum_{i=1}^{5}x_{i}=56 + 60+64 + 80+110=370), and (\bar{x}=\frac{370}{5}=74) (it seems the given mean of 65 in the picture is incorrect). The median of a set with (n = 5) (odd - numbered set) is the (\left(\frac{n + 1}{2}\right))-th value. (\frac{5+1}{2}=3) - rd value, so the median is 64 (the given median of 62 in the picture is incorrect).

Step2: Assume the value added is one of the original values. Let's assume we add a value (x) to the data - set. The new (n=6). The new mean (\bar{y}=\frac{370 + x}{6}), and the new median for an even - numbered set is the average of the (\frac{n}{2})-th and (\left(\frac{n}{2}+1\right))-th ordered values.

Let's assume we add the value 56 again. New sum (S=370 + 56=426). New mean (\bar{y}=\frac{426}{6}=71). The new ordered data set is (56,56,60,64,80,110). The (\frac{6}{2}=3) - rd and (\frac{6}{2}+1 = 4) - th values are 60 and 64. New median (M=\frac{60 + 64}{2}=62).

Answer:

New Mean = 71 New Median = 62