IMathAS-libretexts

In a recent rain storm, the amount of rain that fell was collected at various locations across a county using rain gauges. The amount of rain (measured in inches) is reported below and has been sorted for your convenience.

Rain (inches): 1.4, 1.5, 1.6, 1.8, 2, 2, 2.1, 2.2, 2.2, 2.2, 2.3, 2.4, 2.5

a) Find the mean of this data. (Add them up, divide by how many values there are.) This represents the “average height” or the “typical height” of a student in class.

Mean:

b) Write down your data in order from least to greatest. Try to find the “middle value”. Which height would be right in the middle? This is the median. This value (like the mean) represents an “average height” or a “typical height”.

Median:

c) Find the range of this data. (The largest number minus the smallest number.) This represents how spread out the heights are in the room.

Smallest value (minimum):

Largest value (maximum):

Range:

d) Fill out the frequency table below.

Height	Frequency
[1.35,1.65)
[1.65,1.95)
[1.95,2.25)
[2.25,2.55)

e) Which of the following is the correct histogram for this data?

[Graphs generated by this script: setBorder(47,40,20,5); initPicture(0.83,3.2,0,4);axes(1000,0.5,1,1000,0.5); fill="blue"; stroke="black";line([1.1,-0.08],[1.1,0.08]); text([1.1,0],"1.1","below");line([1.4,-0.08],[1.4,0.08]); text([1.4,0],"1.4","below");line([1.7,-0.08],[1.7,0.08]); text([1.7,0],"1.7","below");line([2,-0.08],[2,0.08]); text([2,0],"2","below");line([2.3,-0.08],[2.3,0.08]); text([2.3,0],"2.3","below");line([2.6,-0.08],[2.6,0.08]); text([2.6,0],"2.6","below");line([2.9,-0.08],[2.9,0.08]); text([2.9,0],"2.9","below");line([3.2,-0.08],[3.2,0.08]); text([3.2,0],"3.2","below");textabs([127.5,0],"Height","above");textabs([0,102.5],"Frequency","right",90);rect([1.1,0],[1.4,1]);rect([1.4,0],[1.7,1]);rect([1.7,0],[2,4]);rect([2,0],[2.3,1]);rect([2.3,0],[2.6,4]);rect([2.6,0],[2.9,1]);rect([2.9,0],[3.2,1]);]
[Graphs generated by this script: setBorder(47,40,20,5); initPicture(1.13,2.9,0,5);axes(1000,1,1,1000,1); fill="blue"; stroke="black";line([1.4,-0.1],[1.4,0.1]); text([1.4,0],"1.4","below");line([1.7,-0.1],[1.7,0.1]); text([1.7,0],"1.7","below");line([2,-0.1],[2,0.1]); text([2,0],"2","below");line([2.3,-0.1],[2.3,0.1]); text([2.3,0],"2.3","below");line([2.6,-0.1],[2.6,0.1]); text([2.6,0],"2.6","below");line([2.9,-0.1],[2.9,0.1]); text([2.9,0],"2.9","below");textabs([127.5,0],"Height","above");textabs([0,102.5],"Frequency","right",90);rect([1.4,0],[1.7,2]);rect([1.7,0],[2,3]);rect([2,0],[2.3,5]);rect([2.3,0],[2.6,2]);rect([2.6,0],[2.9,1]);]

[Graphs generated by this script: setBorder(47,40,20,5); initPicture(1.08,2.55,0,6);axes(1000,1,1,1000,1); fill="blue"; stroke="black";line([1.35,-0.12],[1.35,0.12]); text([1.35,0],"1.35","below");line([1.65,-0.12],[1.65,0.12]); text([1.65,0],"1.65","below");line([1.95,-0.12],[1.95,0.12]); text([1.95,0],"1.95","below");line([2.25,-0.12],[2.25,0.12]); text([2.25,0],"2.25","below");line([2.55,-0.12],[2.55,0.12]); text([2.55,0],"2.55","below");textabs([127.5,0],"Height","above");textabs([0,102.5],"Frequency","right",90);rect([1.35,0],[1.65,3]);rect([1.65,0],[1.95,1]);rect([1.95,0],[2.25,6]);rect([2.25,0],[2.55,3]);]
[Graphs generated by this script: setBorder(47,40,20,5); initPicture(0.53,2.9,0,5);axes(1000,1,1,1000,1); fill="blue"; stroke="black";line([0.8,-0.1],[0.8,0.1]); text([0.8,0],"0.8","below");line([1.1,-0.1],[1.1,0.1]); text([1.1,0],"1.1","below");line([1.4,-0.1],[1.4,0.1]); text([1.4,0],"1.4","below");line([1.7,-0.1],[1.7,0.1]); text([1.7,0],"1.7","below");line([2,-0.1],[2,0.1]); text([2,0],"2","below");line([2.3,-0.1],[2.3,0.1]); text([2.3,0],"2.3","below");line([2.6,-0.1],[2.6,0.1]); text([2.6,0],"2.6","below");line([2.9,-0.1],[2.9,0.1]); text([2.9,0],"2.9","below");textabs([127.5,0],"Height","above");textabs([0,102.5],"Frequency","right",90);rect([0.8,0],[1.1,1]);rect([1.1,0],[1.4,0]);rect([1.4,0],[1.7,0]);rect([1.7,0],[2,3]);rect([2,0],[2.3,5]);rect([2.3,0],[2.6,2]);rect([2.6,0],[2.9,2]);]

f) New Technology: TI-30XS

Now that you have described data again, it is time to add a technology as a calculation tool.

Press the “data” button on the calculator (circled in "pink" at the right), and enter the rainfall data given above. (If there is already data in the list, press data again and clear the lists.)

After entering the data, press 2nd-data (labeled “stat”), and choose 1-Var Stats.

This will report the mean as $\displaystyle \overline{{{x}}}$ . You can scroll down for other calculations. Notice that it tells you the min, the median, and the max. These are other useful calculations.

Once you have the 1-Var Stats displayed on the calculator, as "proof" that you were able to run it, find the line that says $\displaystyle \Sigma{x}^{{2}}=$ and record the value here.

From now on, you are encouraged to use this "1-Var-Stats" capability of the calculator when doing these calculations.

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