Question

chad watched the cashier scan the 6 items in his shopping cart. the scanned prices were: $4.00 $4.00 $4.00 $1.00 $7.00 $1.00 what was the standard deviation of the prices of the items? if the answer is a decimal, round it to the nearest ten cents. standard deviation (σ): $

Explanation:

Step1: Calculate the mean

The mean $\bar{x}$ of a set of numbers $x_1,x_2,\cdots,x_n$ is given by $\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}$.
Here, $n = 6$, $x_1=4,x_2 = 4,x_3=4,x_4=1,x_5=7,x_6=1$.
$\sum_{i=1}^{6}x_i=4 + 4+4 + 1+7+1=21$.
$\bar{x}=\frac{21}{6}=3.5$.

Step2: Calculate the squared - differences

The formula for the variance $\sigma^{2}=\frac{\sum_{i = 1}^{n}(x_i-\bar{x})^{2}}{n}$.
For $x_1 = 4$: $(4 - 3.5)^{2}=0.25$.
For $x_2 = 4$: $(4 - 3.5)^{2}=0.25$.
For $x_3 = 4$: $(4 - 3.5)^{2}=0.25$.
For $x_4 = 1$: $(1 - 3.5)^{2}=6.25$.
For $x_5 = 7$: $(7 - 3.5)^{2}=12.25$.
For $x_6 = 1$: $(1 - 3.5)^{2}=6.25$.
$\sum_{i = 1}^{6}(x_i-\bar{x})^{2}=0.25+0.25+0.25 + 6.25+12.25+6.25=25.5$.

Step3: Calculate the variance and standard deviation

The variance $\sigma^{2}=\frac{25.5}{6}=4.25$.
The standard deviation $\sigma=\sqrt{\sigma^{2}}$.
Since $\sigma^{2}=4.25$, then $\sigma=\sqrt{4.25}\approx2.06$.

Answer:

$2.06$