A factory quality control manager decides to investigate the percentage of defective items produced each day. Within a given work week (Monday through Friday) the proportions of defective items produced were .02, $.014, .04, .03$, and .022 a) Calculate the mean for these data. The mean is 0.0252 b) Calculate the standard deviation for these data. (For a challenge, try to compute the standard deviation by hand. If you would rather not use the standard deviation formula, feel free to use StatsCloud for your calculations.) The standard deviation is

Step 1 ：Given the proportions of defective items produced each day within a work week are 0.02, 0.014, 0.04, 0.03, and 0.022.

Step 2 ：To calculate the mean, we add up all the values and then divide by the number of values. In this case, we have five values.

Step 3 ：\(\text{Mean} = \frac{0.02 + 0.014 + 0.04 + 0.03 + 0.022}{5} = 0.0252\)

Step 4 ：To calculate the standard deviation, we first need to calculate the variance. The variance is the average of the squared differences from the mean.

Step 5 ：First, subtract the mean from each value to get the difference, square each difference, add up all the squared differences, and then divide by the number of values to get the variance.

Step 6 ：\(\text{Variance} = \frac{(0.02 - 0.0252)^2 + (0.014 - 0.0252)^2 + (0.04 - 0.0252)^2 + (0.03 - 0.0252)^2 + (0.022 - 0.0252)^2}{5}\)

Step 7 ：The standard deviation is then the square root of the variance.

Step 8 ：\(\text{Standard Deviation} = \sqrt{\text{Variance}} = 0.009\)

Step 9 ：Final Answer: The mean of the data is \(\boxed{0.0252}\) and the standard deviation is \(\boxed{0.009}\).