Question

each of the 6 cats in a pet store was weighed. here are their weights (in pounds).
13, 5, 16, 5, 8, 16
find the median and mean weights of these cats.
if necessary, round your answers to the nearest tenth.
(a) median: □ pounds
(b) mean: □ pounds

Explanation:

Step1: Find the Median

First, we need to order the data set from least to greatest: \(5, 5, 8, 13, 16, 16\). Since there are 6 (an even number) data points, the median is the average of the two middle numbers. The two middle numbers are the 3rd and 4th values, which are 8 and 13. So, the median is \(\frac{8 + 13}{2}\).
\(\frac{8 + 13}{2}=\frac{21}{2} = 10.5\)

Step2: Find the Mean

The mean is calculated by summing all the values and dividing by the number of values. The sum of the weights is \(13 + 5 + 16 + 5 + 8 + 16\). Let's calculate that: \(13+5 = 18\), \(18+16 = 34\), \(34+5 = 39\), \(39+8 = 47\), \(47+16 = 63\). There are 6 cats, so the mean is \(\frac{63}{6}\).
\(\frac{63}{6}=10.5\)

Answer:

(a) Median: \(10.5\) pounds
(b) Mean: \(10.5\) pounds