Question

the average weekly unemployment benefits (in dollars) for a random selection of states are listed below. 272 239 289 214 276 252 190 209 251 272 310 321 327 356 416 send data to excel part: 0 / 3 part 1 of 3 find the standard deviation. round your answer to at least one decimal place. the standard deviation is

Explanation:

Step1: Calculate the mean

Let the data set be $x_1,x_2,\cdots,x_n$. Here $n = 16$, and $\sum_{i = 1}^{16}x_i=272 + 239+289+214+276+252+190+209+251+272+310+321+327+356+416 = 4294$. The mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}=\frac{4294}{16}=268.375$.

Step2: Calculate the squared - differences

For each data point $x_i$, calculate $(x_i-\bar{x})^2$. For example, for $x_1 = 272$, $(272 - 268.375)^2=(3.625)^2 = 13.140625$. Do this for all 16 data points and sum them up. $\sum_{i = 1}^{16}(x_i - 268.375)^2=13.140625+(239 - 268.375)^2+(289 - 268.375)^2+\cdots+(416 - 268.375)^2=29997.875$.

Step3: Calculate the variance

The variance $s^2=\frac{\sum_{i = 1}^{n}(x_i-\bar{x})^2}{n - 1}$. Substituting $n = 16$ and $\sum_{i = 1}^{16}(x_i-\bar{x})^2=29997.875$, we get $s^2=\frac{29997.875}{15}\approx1999.8583$.

Step4: Calculate the standard deviation

The standard deviation $s=\sqrt{s^2}=\sqrt{1999.8583}\approx44.7$.

Answer:

$44.7$