Question

basic measures of center -2
score: 11.88/23 answered: 1/4
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question 2
7 pts 1 2 details
use the appropriate formulas and methods to answer the following questions. do not use technology as an aid, unless otherwise stated.
part 1 of 6
hint 1 hint 2 hint 3 hint 4 hint 5
consider the following sample data, which represent weights walnuts in grams:
{ 13.2, 13.2, 14.1, 14.1, 14.3, 14.4, 14.4, 14.4, 14.9, 15.8, 16, 16, 16.1, 16.2, 17.4, 17.5, 18.4, 18.6, 19.2 , 20.9 }.
first, give the mean of the data set.

Explanation:

Step1: Recall the mean formula

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

Step2: Count the number of data points

Count the number of values in the data - set $\{13.2, 13.2, 14.1, 14.1, 14.3, 14.4, 14.4, 14.4, 14.9, 15.8, 16, 16, 16.1, 16.2, 17.4, 17.5, 18.4, 18.6, 19.2, 20.9\}$. Here, $n = 20$.

Step3: Calculate the sum of the data points

\[

$$\begin{align*} \sum_{i = 1}^{20}x_i&=13.2\times2 + 14.1\times2+14.3 + 14.4\times3+14.9+15.8+16\times2+16.1+16.2+17.4+17.5+18.4+18.6+19.2+20.9\\ &=26.4+28.2 + 14.3+43.2+14.9+15.8+32+16.1+16.2+17.4+17.5+18.4+18.6+19.2+20.9\\ &=(26.4 + 28.2)+14.3+43.2+14.9+15.8+32+16.1+16.2+17.4+17.5+18.4+18.6+19.2+20.9\\ &=54.6+14.3+43.2+14.9+15.8+32+16.1+16.2+17.4+17.5+18.4+18.6+19.2+20.9\\ &=(54.6+14.3)+43.2+14.9+15.8+32+16.1+16.2+17.4+17.5+18.4+18.6+19.2+20.9\\ &=68.9+43.2+14.9+15.8+32+16.1+16.2+17.4+17.5+18.4+18.6+19.2+20.9\\ &=(68.9 + 43.2)+14.9+15.8+32+16.1+16.2+17.4+17.5+18.4+18.6+19.2+20.9\\ &=112.1+14.9+15.8+32+16.1+16.2+17.4+17.5+18.4+18.6+19.2+20.9\\ &=(112.1+14.9)+15.8+32+16.1+16.2+17.4+17.5+18.4+18.6+19.2+20.9\\ &=127+15.8+32+16.1+16.2+17.4+17.5+18.4+18.6+19.2+20.9\\ &=(127+15.8)+32+16.1+16.2+17.4+17.5+18.4+18.6+19.2+20.9\\ &=142.8+32+16.1+16.2+17.4+17.5+18.4+18.6+19.2+20.9\\ &=(142.8+32)+16.1+16.2+17.4+17.5+18.4+18.6+19.2+20.9\\ &=174.8+16.1+16.2+17.4+17.5+18.4+18.6+19.2+20.9\\ &=(174.8+16.1)+16.2+17.4+17.5+18.4+18.6+19.2+20.9\\ &=190.9+16.2+17.4+17.5+18.4+18.6+19.2+20.9\\ &=(190.9+16.2)+17.4+17.5+18.4+18.6+19.2+20.9\\ &=207.1+17.4+17.5+18.4+18.6+19.2+20.9\\ &=(207.1+17.4)+17.5+18.4+18.6+19.2+20.9\\ &=224.5+17.5+18.4+18.6+19.2+20.9\\ &=(224.5+17.5)+18.4+18.6+19.2+20.9\\ &=242+18.4+18.6+19.2+20.9\\ &=(242+18.4)+18.6+19.2+20.9\\ &=260.4+18.6+19.2+20.9\\ &=(260.4+18.6)+19.2+20.9\\ &=279+19.2+20.9\\ &=(279+19.2)+20.9\\ &=298.2+20.9\\ &=319.1 \end{align*}$$

\]

Step4: Calculate the mean

Using the formula $\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}$, substitute $n = 20$ and $\sum_{i=1}^{20}x_i = 319.1$. So, $\bar{x}=\frac{319.1}{20}=15.955$.

Answer:

$15.955$