Question

use the appropriate formulas and methods to answer the following questions. do not use technology as an aid, unless otherwise stated. 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. next, give the median of the data set.

Explanation:

Step1: Recall mean formula

The mean $\bar{x}$ of a data - set $x_1,x_2,\cdots,x_n$ is given by $\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}$, where $n$ is the number of data points and $\sum_{i=1}^{n}x_i$ is the sum of the data points.

Step2: Calculate the sum of data points

$\sum_{i = 1}^{20}x_i=10.6 + 10.9+11.6+11.7+12.9+13.5+13.5+14+14+14+14.4+14.6+14.9+15.4+16.3+16.6+17.2+17.2+17.8+18.5 = 286.3$.

Step3: Calculate the number of data points

$n = 20$.

Step4: Calculate the mean

$\bar{x}=\frac{286.3}{20}=14.315$.

Step5: Recall median formula for even - numbered data set

For a data - set with $n$ (even) data points, after arranging the data in ascending order, the median $M$ is the average of the $\frac{n}{2}$ - th and $(\frac{n}{2}+1)$ - th ordered data points.

Step6: Arrange data in ascending order

The data is already in ascending order.

Step7: Identify the middle positions

Since $n = 20$, $\frac{n}{2}=10$ and $\frac{n}{2}+1 = 11$.

Step8: Find the 10 - th and 11 - th data points

The 10 - th data point is $14$ and the 11 - th data point is $14.4$.

Step9: Calculate the median

$M=\frac{14 + 14.4}{2}=\frac{28.4}{2}=14.2$.

Answer:

Mean: $14.315$
Median: $14.2$