the following are a students five exam scores: 77,72,63,62,68. calculate the mean: $\bar{x}=$. calculate the…

the following are a students five exam scores: 77,72,63,62,68. 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.

the following are a students five exam scores: 77,72,63,62,68. 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.

Answer

Explanation:

Step1: Calculate the mean

The data set is (77,72,63,62,68). The formula for the mean (\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}), where (n = 5) and (x_{i}) are the data - points. (\bar{x}=\frac{77 + 72+63+62+68}{5}=\frac{342}{5}=68.4)

Step2: Calculate ((x-\bar{x})) for each data - point

For (x = 77): (77−68.4 = 8.6) For (x = 72): (72−68.4 = 3.6) For (x = 63): (63−68.4=-5.4) For (x = 62): (62−68.4=-6.4) For (x = 68): (68−68.4=-0.4)

Step3: Calculate ((x - \bar{x})^2) for each data - point

For (x = 77): ((77 - 68.4)^2=(8.6)^2 = 73.96) For (x = 72): ((72 - 68.4)^2=(3.6)^2 = 12.96) For (x = 63): ((63 - 68.4)^2=(-5.4)^2 = 29.16) For (x = 62): ((62 - 68.4)^2=(-6.4)^2 = 40.96) For (x = 68): ((68 - 68.4)^2=(-0.4)^2 = 0.16)

Step4: Calculate the sum of ((x-\bar{x})^2)

(\sum_{i = 1}^{5}(x_{i}-\bar{x})^2=73.96 + 12.96+29.16+40.96+0.16=157.2)

Step5: Calculate the standard deviation

The formula for the sample standard deviation is (s=\sqrt{\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^2}{n - 1}}), with (n = 5). (s=\sqrt{\frac{157.2}{4}}=\sqrt{39.3}\approx6.27)

Answer:

Mean: (68.4) Standard deviation: (6.27)