Organizing and Summarizing Data

Tally sheets

Lesson Overview

Goals

Students will be able to group data values and count like values.

Students will be able to read a word problem and create a tally sheet from the information provided.

Instructor Presentation

Introduction

When data is collected, we often want to determine how the individual data elements relate to one another and to the whole data set. This lesson plan outlines several common techniques to help turn raw data into information using tally sheets.
Lets start with a small data set consisting of the number of goals made by a soccer player in each game from the last season.

goals={1,0,2,1,0,1,0,2,0,1,2,5,0,2,0,0,3,1,1,2,0,0,3}

What I would like to know is in how many games did she make three goals.
With the list above, it is not easy to determine this.  So, what we should do first is to sort the data from lowest value to highest value.

goalssorted=Sort[goals]

Once we have the data sorted, it is quite easy to create a tally sheet.

tallytable=Table[{n,Count[goalssorted,n]},{n,0,5}];
fulldata=Prepend[tallytable,{"Goals Scored","Games"}];
DisplayTable[fulldata,TableLabel->"Goals Scored Per Game",ItemSize->13]

(Labeled[({{"Goals Scored", "Games"}, {0, 9}, {1, 6}, {2, 5}, {3, 2}, {4, 0}, {5, 1}}), "Goals Scored Per Game"])

Lets look at another one:
The leader of the Cheerleader squad wants to know how many different cheers are performed during a football game.  During the season, she counts the following cheers performed:

cheers={8,10,12,11,9,11,9,10,11}

What she would like to know is how many cheers are performed.
With the list above, it is not easy to determine this.  So, what we should do first is to sort the data from lowest value to highest value.

cheerssorted=Sort[cheers]

Once we have the data sorted, it is quite easy to create a tally sheet.

tallytable1=Table[{n,Count[cheerssorted,n]},{n,7,13}];
fulldata1=Prepend[tallytable1,{"Cheers Performed","Games"}];
DisplayTable[fulldata1,TableLabel->"Cheers Performed Per Game",ItemSize->13]

(Labeled[({{"Cheers Performed", "Games"}, {7, 0}, {8, 1}, {9, 2}, {10, 2}, {11, 3}, {12, 1}, {13, 0}}), "Cheers Performed Per Game"])

According to the USA Today newspaper, the average number of cheers that a Cheerleading squad does in a game is 12.   If you were the Cheerleading Leader, what would you do?

Concept Exploration

Steps

There are three steps to creating a tally sheet.

Sort the data elements from lowest to highest

Count the data elements

Put the data elements and counts into a table

Examples

Example 1

According to McDonalds, a serving of their small fries should weigh 2.5 ounces. Sally wanted to know if this was accurate, so each time she went to McDonalds during the year, she recorded the weight of her small fries. The following weights were recorded:

weightfries=
{2.6,2.4,2.5,2.6,2.7,2.2,2.4,2.5,2.6,2.7,2.6,2.5,2.4,2.6,2.5,2.6,2.7}

1: Sort the data elements from low to high

weightfriessorted=Sort[weightfries]

2: Count the data elements

Tally[weightfriessorted]

3: Put the data elements and counts into a table

friestallytable=Table[{n,Count[weightfriessorted,n]},{n,2.2,2.9,.1}];
friesdata=Prepend[friestallytable,{"Weight of Fries","Number of Bags"}];
DisplayTable[friesdata,TableLabel->"Weight of Fries per Bag",ItemSize->13]

(Labeled[({{"Weight of Fries", "Number of Bags"}, {2.2`, 1}, {2.3000000000000003`, 0}, {2.4000000000000004`, 3}, {2.5`, 4}, {2.6`, 6}, {2.7`, 3}, {2.8000000000000003`, 0}, {2.9000000000000004`, 0}}), "Weight of Fries per Bag"])

Example 2

Lets give it a try with a smaller data set.

Your mathematics teacher graded the last test and determined the following grades:  A,C,D,B,B,A,C,B,C,A,D,B,C,C,C,B,A. Create a tally sheet for the grades.

1: Sort the data elements

grades=Sort[{A,C,D,B,B,A,C,B,C,A,D,B,C,C,C,B,A}]

2: Count the data elements

2.  Count the number of data elements

gradessorted=Tally[grades]

3: Put the data elements and counts into a table

gradesdata=Prepend[gradessorted,{"Grade","Number of Tests"}];
DisplayTable[gradesdata,TableLabel->"Results of Last Test",ItemSize->13]

(Labeled[({{"Grade", "Number of Tests"}, {A, 4}, {B, 5}, {C, 6}, {D, 2}}), "Results of Last Test"])

Student Exercises

Exercise 1

The teachers as Polo Middle School are all quite busy.  They teach a lot of courses.  Here is a list of the number of course each teacher teaches  { 6,5,7,5,3,7,6,6,8,5,7,5,4,6 } .  Create a tally sheet for the number of classes taught by the teachers.

Answer:

classestaught={6,5,7,5,3,7,6,6,8,5,7,5,4,6}

Sort[classestaught]

classtally=Tally[Sort[classestaught]]

classesdata=Prepend[classtally,{"Classes Taught","Number of Teachers"}];
DisplayTable[classesdata,TableLabel->"Number of Class Taught by Teacher",ItemSize->13]

(Labeled[({{"Classes Taught", "Number of Teachers"}, {3, 1}, {4, 1}, {5, 4}, {6, 4}, {7, 3}, {8, 1}}), "Number of Class Taught by Teacher"])

Exercise 2

Mary is very good at jumping rope.  Mary can jump rope very quickly.  In fact, Mary can jump rope 64 times in a minute.  Given that Mary's fellow students can jump rope as follows {54,58,38,58,49,55,61,64,58,59,60,61,66,62,59,57,55}.   Should Mary enter the school jump roping contest?

Answer:

jumproping={54,58,38,58,49,55,61,64,58,59,60,61,66,62,59,57,55}

Sort[jumproping]

jumptally=Tally[Sort[jumproping]]

jumpdata=Prepend[jumptally,{"Ropes Jumped","Number of Students"}];
DisplayTable[jumpdata,TableLabel->"Number of Ropes Jumped in a Minute",ItemSize->13]

(Labeled[({{"Ropes Jumped", "Number of Students"}, {38, 1}, {49, 1}, {54, 1}, {55, 2}, {57, 1}, {58, 3}, {59, 2}, {60, 1}, {61, 2}, {62, 1}, {64, 1}, {66, 1}}), "Number of Ropes Jumped in a Minute"])

Initializations

DisplayTable[data_List,opts:OptionsPattern[]]:=CellPrint[TextCell[Labeled[Grid[data,FilterRules[{opts},Options[Grid]],Frame->All,ItemSize->14,Alignment->Center,BaseStyle->{FontFamily->"Helvetica",FontSize->18},Background->LightYellow,Frame->All,Spacings->{2,0.62}],Style[OptionValue[TableLabel],FontFamily->"Times", 16]],"DisplayFormula",ShowStringCharacters->False]]