Question

the monthly rents (in dollars) paid by 9 people are given below. (note that these are already ordered from least to greatest.) 845, 900, 905, 920, 930, 970, 995, 1035, 1140. suppose that one of the people moves. his rent changes from $1140 to $960. answer the following. (a) what happens to the median? it stays the same. it increases by $. it decreases by $. (b) what happens to the mean? it stays the same. it increases by $. it decreases by $. send data to calculator

Explanation:

Step1: Recall the formula for the median of 9 - data points

For a set of 9 ordered data - points, the median is the 5th value. Since the data is already ordered (845, 900, 905, 920, 930, 970, 995, 1035, 1140), the median is 930. When the value 1140 changes to 960, the new ordered set is 845, 900, 905, 920, 930, 960, 970, 995, 1035. The median is still the 5th value, which is 930. So the median stays the same.

Step2: Recall the formula for the mean

The mean of a set of data \(x_1,x_2,\cdots,x_n\) is \(\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}\). The original sum of the 9 - data points \(S_1=845 + 900+905 + 920+930+970+995+1035+1140=8640\), and the original mean \(\bar{x}_1=\frac{8640}{9}\approx960\). The new sum of the 9 - data points \(S_2=845 + 900+905 + 920+930+960+970+995+1035=8460\), and the new mean \(\bar{x}_2=\frac{8460}{9}=940\). The change in the mean is \(960 - 940=20\), so the mean decreases by 20.

Answer:

(a) It stays the same.
(b) It decreases by 20.