Question

1. home prices in a neighborhood vary every year. in 2021, the following ten home prices were listed (in thousands): h 120 166 173 h h h 123 127 l where l indicates a home below $110 and h indicates a home above $190. the median home price is (a) 166 (b) 169.5 (c) 170 (d) 173 (e) cannot be determined

Explanation:

Step1: Arrange data in order

We have 10 data - points. Let's assume the order from smallest to largest. We know L < 110, and H>190. The ordered list of known non - H and non - L values is 120, 123, 127, 166, 173. Since there are 10 data points, the median is the average of the 5th and 6th ordered data points.

Step2: Determine position of median

For a set of \(n = 10\) data points, the median position is \(\frac{n}{2}=5\) and \(\frac{n}{2}+ 1=6\). We need to find the 5th and 6th values in the ordered set.

Step3: Identify median values

We know that when we order all 10 values, the 5th and 6th values (in order) among the 10 values will be 166 and 173 (because the L values are the smallest and H values are the largest).

Step4: Calculate median

The median of a set with \(n = 10\) (an even number of data points) is \(\text{Median}=\frac{166 + 173}{2}=\frac{339}{2}=169.5\)

Answer:

B. 169.5