Standard Deviation

We started section 5.3 today. We got a hand out and did the following question together:

"The coach of a girls' basketball team keeps stats on all of the players. Near the end of one game, the score is tied and the starting point guard gets fouled out. He needs to make a substitution. There are five girls on the bench who can sub in for the point guard."
The stats for the players were stated next.

Then we were asked which player was most consistent. We found that Paige was most consistent because her percentages were all between 33-35. They were not scattered, therefore they were consistent.

After that it said that the coach found that Paige and Patrice's values were close in value. He compared them more closely using standard deviation (a measure of the dispersion or scatter of data values in relation to the mean.)

We followed these steps to calculate the standard deviation for Paige:
-Determine the mean of Paige's shooting percentage.
(add all of Paige's percentages then divide by the amount of percentages there is. In this case there is ten.) We found that Paige's mean was 33.9.

-Calculate the deviation of each field goal percentage.
(Take one percentage and subtract it from the mean. Continue doing this with all the percentages.)
EX. 34-33.9=.1

-Calculate the squares of the deviations.
EX. The square root of .1 is .01. (Square root all deviations.)

-Fill in the values into the chart on the second page of the handout.

-Determine the standard deviation by:
-determining the mean of the squares of deviations.
(add all the squares of deviations and divide by 10)
Our answer was .69

-determining the square root of the mean from the step above^:
The square root of .69 is .8307.

Then we did the steps above for Patrice.
Next, we were asked who was more consistent between the two players. Our answer was Paige because .8307 is a smaller standard deviation than 1.4976(Patrice's standard deviation) and a smaller number means that here is more consistency.

We then calculated the mean and standard deviation using a graphing calculator. To do this, you must follow these steps:
-Stat
-Edit
-Enter the numbers
-Stat
-Calc
-1-var stats
-Enter.
(I probably forgot a step.)

We didn't finish the whole sheet but we will be finishing the rest in class tomorrow.
Next up is Colby.