Question

basic measures of center -2
score: 5.94/23 answered: 1/4
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question 2
7 pts 1 4 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:
{7, 12.2, 12.3, 12.5, 13.8, 13.9, 14.2, 14.3, 14.5, 14.8, 14.9, 15.7, 16.1, 16.2, 18.1, 18.3, 18.6, 18.6, 18.7, 19.5}.
first, give the mean 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: Count number of data points

Count the number of values in the data - set $\{7, 12.2, 12.3, 12.5, 13.8, 13.9, 14.2, 14.3, 14.5, 14.8, 14.9, 15.7, 16.1, 16.2, 18.1, 18.3, 18.6, 18.6, 18.7, 19.5\}$. Here, $n = 20$.

Step3: Calculate the sum of data points

$7+12.2 + 12.3+12.5+13.8+13.9+14.2+14.3+14.5+14.8+14.9+15.7+16.1+16.2+18.1+18.3+18.6+18.6+18.7+19.5$
$=(7)+(12.2 + 12.3+12.5)+(13.8+13.9)+(14.2+14.3+14.5+14.8+14.9)+(15.7+16.1+16.2)+(18.1+18.3+18.6+18.6+18.7+19.5)$
$=7+(37)+(27.7)+(70.7)+(48)+(101.8)$
$=292.2$.

Step4: Calculate the mean

$\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}=\frac{292.2}{20}=14.61$.

Answer:

$14.61$