How to Compute a Population Mean and Sample Mean (Section 3.1 topic).doc

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Computing a Population Mean and Sample Mean

The data in the table bellow represents the number of home runs hit by all teams in the American League in 2001.

Team	Home Runs	Team	Home Runs
1. Anaheim Angels	158	8. Minnesota Twins	164
2. Baltimore Orioles	136	9. New York Yankees	203
3. Boston Red Sox	198	10. Oakland Athletics	199
4. Chicago White Sox	214	11. Seattle Mariners	169
5. Cleveland Indians	212	12. Tampa Bay Devil Rays	121
6. Detroit Tigers	139	13. Texas Rangers	246
7. Kansas City Royals	152	14. Toronto Blue Jays	195

(a) compute the population mean.

(b) Find a simple random sample of size n = 5

The TI-83 has one method for calculating the mean of a dataset. This method is used for a population mean,, and a sample mean,. The calculator always used, the symbol for the sample mean.

(a.) Press STAT and select 1: Edit. Clear L1 and enter the data into L1. Press STAT again and highlight CALC to view the Calc Menu.

Select 1:1 – Var Stats. On this line, enter the name of the column that contains the data. Since you have stored the data in L1, simply enter 2^nd ENTER and the first page of the one variable statistics will appear. (Note: if you did not enter a column name, the default column, which is L1, would automatically selected.)

The first item is the mean of the dataset. The correct symbol for the mean of a population is. For this dataset,.

(b.) To use a seed of ‘55’, press 55 STO MATH and select PRB. Press ENTER to select 1:Rand and press ENTER. (Note: Selecting a seed is optional step which can be omitted when generating random data.)

To generate a random sample of 5 teams from the 14 teams, Press MATH and select PRB. Select 5: RandInt by pressing 5 or moving the cursor to 5: RandInt. Enter starting value of 1, and ending value of 14 and a sample size of 7. (Recall: The TI-83 samples with replacement. This method may result in duplicates in your sample. Selecting a few more values than you need will allow you to skip duplicate values.)

In this outcome there were no duplicates. The random sample of 5 teams would be the first 5 numbers: 1, 2, 6, 12, and 11. (Note: if you had not selected ‘55’ as the see you would have obtained a different set of numbers.)

(c.) Press STAT and select 1: Edit. Clear L2 and enter the 5 data values into L2. Press STAT again and highlight CALC to view the Calc Menu. Select 1:1 Var Stats. On this line, enter the name of the column that contains the data. Since you have stored the data in L2, simply enter 2^nd ENTER and the first 0page of the one variable statistics will appear.

The sample mean,, is 144.6.