Question

score on last try: 0 of 1 pts. see details for more. at least one scored part is incorrect. jump to first changeable incorrect part. > next question you can retry this question below the following are a students five exam scores. 66,73,80,79,63 calculate the mean: $\bar{x}=$ calculate the standard deviation, the long way. fill in the values in the table below. using $s = sqrt{\frac{sum(x - \bar{x})^2}{n - 1}}$ what is the standard deviation? (take the total from the table, divide by n - 1 and then find the square root) round your answer to 2 decimal places. s =

Explanation:

Step1: Calculate the mean

The mean $\bar{x}=\frac{66 + 73+80+79+63}{5}=\frac{361}{5}=72.2$

Step2: Calculate $(x - \bar{x})^2$ for each $x$

For $x = 66$: $(66 - 72.2)^2=(-6.2)^2 = 38.44$
For $x = 73$: $(73 - 72.2)^2=(0.8)^2=0.64$
For $x = 80$: $(80 - 72.2)^2=(7.8)^2 = 60.84$
For $x = 79$: $(79 - 72.2)^2=(6.8)^2=46.24$
For $x = 63$: $(63 - 72.2)^2=(-9.2)^2 = 84.64$

Step3: Calculate the total of $(x - \bar{x})^2$

$\sum(x - \bar{x})^2=38.44 + 0.64+60.84+46.24+84.64=230.8$

Step4: Calculate the standard - deviation

$n = 5$, so $s=\sqrt{\frac{\sum(x - \bar{x})^2}{n - 1}}=\sqrt{\frac{230.8}{4}}=\sqrt{57.7}\approx7.60$

Answer:

Mean: $\bar{x}=72.2$
For $x = 66$: $(x-\bar{x})^2 = 38.44$
For $x = 73$: $(x-\bar{x})^2 = 0.64$
For $x = 80$: $(x-\bar{x})^2 = 60.84$
For $x = 79$: $(x-\bar{x})^2 = 46.24$
For $x = 63$: $(x-\bar{x})^2 = 84.64$
Total $\sum(x - \bar{x})^2=230.8$
Standard - deviation $s\approx7.60$