D.3.:  Stat Analysis and Curve Fitting

The features described below are useful in computing statistical variables such as the mean, ∑x, ∑x2, sx (sample standard deviation), sx (population standard deviation), n (sample size), Q1(First Quartile), Med (2nd Quartile), Q3 (Third Quartile), Min, Max for x and y variables.

The values calculated are also stored in the VARS menu which can be accessed by pressing VARS … 5:Statistics, selected the desired variable, press ENTER…ENTER.

D.3.1.:  1-Var Stats

1.  Compute the statistics of one variable: Let’s use the data for the height in inches of 10 female high school seniors:    62, 67, 58, 60, 66, 65, 69, 69, 74, 76 and input in L1 (clear all lists before you input this data!).  Compute the mean, median, sample standard deviation, Q1, Q3, min and max for this data.

1.)    Input data in L1 and QUIT

2.)    Press STAT

3.)    Select CALC

4.)    ENTER (default is L1)

5.)    ENTER

6.)    Use down arrow key to get the rest of the statistical variables.   (1)                       (2)                         (3)   (4)  default L1                (5)                            (6)

Results:  The mean is 66.6 in., sample std. deviation is 5.7387… in., sample size is 10, the minimum is 58 in., first quartile is 62 in., median is 66.5 in., third quartile is 69 in., and maximum is 76 in.  All these values will also be stored in the VARS menu. Check it!

Activity:  Compute all statistical variables for the calorie consumption data:  The number of calories consumed daily by a sample of 14 adults are as follows:  2340, 1200, 1500, 2900, 800, 3100, 1450, 2500, 1800, 3600, 3200, 2400, 2200, 1600.

2. Compute the Weighted Mean:

Let’s assume you are a shrimp lover and you have purchased various amounts of shrimp at different stores and markets at varying prices. In the end you would like to know how much on average you paid for one pound of jumbo shrimp.  Over the last three months, you have purchased the following:  3 lbs. at \$6.33 per pound, 5 lbs at \$5.29 per pound, 10 lbs at \$5.99 per pound, 2 lbs at \$7.49 per pound and 6 lbs at \$5.49 per pound.  How much on average did you pay per pound?

Let x = the price of shrimp and y= the amount of shrimp. Input these values in L1 and L2.

Find the weighted mean:

1.)    Input data in L1 and L2, then QUIT

2.)    Press STAT

3.)    Select CALC and select 1-Var Stats

4.)    ENTER and type L1, L2

5.)    ENTER

Use down arrow key to get the rest of the statistical variables.    Hence, the average price per pound is \$5.89.

Manual Computation:

3(6.33) + 5(5.29) + 10(5.99) + 2(7.49) + 6(5.49)  =  5.8946…

3 + 5 + 10 + 2  + 6

Activity:  During the following 7 days you have been online writing as many emails as possible to inform your friends of the upcoming graduation party.  The following are the lengths of time online and the numbers of letters written:  Monday 5 min, 16 letters; Tuesday 15 min, 24 letters;  Wednesday 8 min, 6 letters; Thursday 2 min, 3 letters; Friday 25 min, 18 letters; Saturday 1 hour, 35 letters; and Sunday 20 min, 7 letters.

D.3.2.:  2-Var Stats

Compute the statistics of two variables: The two-variable statistics feature is helpful if you are dealing with two variables at the same time, i.e. height and weight.

For example, we collected more data on the high school girls. Each girl was asked about their weight and the following was recorded:

 Height (in.) Weight (lbs.) 62 105 67 124 58 120 60 90 66 130 65 120 69 162 69 134 74 122 76 185

Compute the statistical variables for the height and the weight of the girls.

Use the same procedure as above but you need to select 2-Var Stats and indicate where you store the data, namely L1, L2.

1.)  Input data in L1 and L2 then QUIT

2.)    Press STAT

3.)    Select CALC and 2-Var Stats

4.)    ENTER and type L1, L2  (default is L1 and L2)

5.)    ENTER

6.)    Use down arrow key to get the rest of the statistical variables.     This will provide you will all the statistical variables for height and weight. Again these variables are stored in the VARS menu and you can recall them any time.