Question

each of the 8 cats in a pet store was weighed. here are their weights (in pounds). 13, 11, 6, 11, 13, 5, 6, 14 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: Sort the data

5, 6, 6, 11, 11, 13, 13, 14

Step2: Calculate the median

Since there are 8 data - points ($n = 8$, an even number), the median is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+1)$th ordered values. $\frac{n}{2}=4$ and $\frac{n}{2}+1 = 5$. The 4th value is 11 and the 5th value is 11. Median=$\frac{11 + 11}{2}=11$.

Step3: Calculate the mean

The mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, where $x_{i}$ are the data - points and $n = 8$. $\sum_{i=1}^{8}x_{i}=5 + 6+6 + 11+11+13+13+14=79$. Mean=$\frac{79}{8}=9.875\approx9.9$.

Answer:

(a) 11 pounds
(b) 9.9 pounds