Question

consider the following sample data, which represent weights walnuts in grams: { 10.6, 10.9, 11.6, 11.7, 12.9, 13.5, 13.5, 14, 14, 14, 14.4, 14.6, 14.9, 15.4, 16.3, 16.6, 17.2, 17.2, 17.8 , 18.5 }. first, give the mean of the data set. part 2 of 6 next, give the median of the data set. part 3 of 6 now give the mode of the data set. if there is more than one, write them in order, separated by commas.

Explanation:

Step1: Recall the formula for the mean

The mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, where $x_{i}$ are the data - points and $n$ is the number of data - points. Here, $n = 20$.
$\sum_{i=1}^{20}x_{i}=10.6 + 10.9+11.6+11.7+12.9+13.5+13.5+14+14+14+14.4+14.6+14.9+15.4+16.3+16.6+17.2+17.2+17.8+18.5=283.3$
$\bar{x}=\frac{283.3}{20}=14.165$

Step2: Recall the formula for the median

Since $n = 20$ (an even number), the median is the average of the $\frac{n}{2}$ - th and $(\frac{n}{2}+1)$ - th ordered data - points. The data is already ordered. $\frac{n}{2}=10$ and $\frac{n}{2}+1 = 11$. The 10 - th value is 14 and the 11 - th value is 14.4. Median $=\frac{14 + 14.4}{2}=14.2$

Step3: Recall the formula for the mode

The mode is the data - point(s) that occur(s) most frequently. In the data set, 14 occurs 3 times and 13.5 and 17.2 each occur 2 times, and all other values occur only once. So the mode is 14.

Answer:

Part 1: 14.165
Part 2: 14.2
Part 3: 14