Question

Dr. Cwetna recorded all of the grades on a unit test on the chart below. 1. What is the mean and standard deviation of the distribution of individual grades? (30 point) x = _______ 82.75 ________ σ = _____ 10.65 __________ 2. In your own words, explain HOW to find the standard deviation of this data set. (20 points) 3. What does the standard deviation tell you about this data? (20 points) PLSSSSS I NEED THIS BY TODAY PLSSSSSSSSSSSSSSSS

Answer 1

1) From the given information, the mean and standard deviation re determined as
`\bar x` = 82.75 and σ = 10.65

2)
`\sigma =\sqrt{\frac{\sum \left (x - \bar{x} \right )^(2)}{n}}`

3) That 95% of the grades are between the values of 72.1 and 93.4

Explanation:

1) From the given information, the mean and standard deviation re determined as
`\bar x` = 82.75 and σ = 10.65

2) To find the standard deviation

a) We find the mean,
`\bar x` by summing the data, x, and dividing the summation by the the number of data points, n

b) From each of the data, the mean is subtracted and the difference is squared (multiplied by itself)

c) The mean of the squares from above is found by adding them together and dividing by the number of data points

d) The square root of the mean of the squares from the previous step is then found and that is the standard deviation

3) The standard deviation tells how varied the data in the population is and the standard deviation of 10.65 in the question tells us that 95% of the grades are between 82.75 - 10.65 and 82.75 + 10.65 which is the range between 72.1 and 93.4.