once we gather our data we need a way to represent our findings. one way to do this is through the...

ORGANIZING DATA

Once we gather our data we need a way to represent our findings. One way to do this is through the use of a Frequency Distribution.

ORGANIZING DATA


A frequency distribution or frequency table partitions data into classes or intervals. It shows how many data values are in each class. The classes or intervals are constructed so that data values can only appear in one class.

ORGANIZING DATA



To create a frequency table you will :

a) decide how many classes or intervals you want to use. ( 5 to 15 classes are usually used )

ORGANIZING DATA



To create a frequency table you will :

a) decide how many classes or intervals you want to use. ( 5 to 15 classes are usually used )

b) determine the class width ( what range will the data be separated )

ORGANIZING DATA

EXAMPLE : Here is a table of mileage that workers travel for a one – way commute to their job.

13 47 10 3 16 20 17 40 4 2

7 25 8 21 19 15 3 17 14 6

12 45 1 8 4 16 11 18 23 12

6 2 14 13 7 15 46 12 9 18

34 15 41 28 36 17 24 27 29 9

14 26 10 24 37 31 8 16 12 16

ORGANIZING DATA


13 47 10 3 16 20 17 40 4 2

7 25 8 21 19 15 3 17 14 6

12 45 1 8 4 16 11 18 23 12

6 2 14 13 7 15 46 12 9 18

34 15 41 28 36 17 24 27 29 9

14 26 10 24 37 31 8 16 12 16

Let’s use 6 data intervals

ORGANIZING DATA


13 47 10 3 16 20 17 40 4 2

7 25 8 21 19 15 3 17 14 6

12 45 1 8 4 16 11 18 23 12

6 2 14 13 7 15 46 12 9 18

34 15 41 28 36 17 24 27 29 9

14 26 10 24 37 31 8 16 12 16


The largest commuting value is 47 and the shortest is 1.

ORGANIZING DATA


13 47 10 3 16 20 17 40 4 2

7 25 8 21 19 15 3 17 14 6

12 45 1 8 4 16 11 18 23 12

6 2 14 13 7 15 46 12 9 18

34 15 41 28 36 17 24 27 29 9

14 26 10 24 37 31 8 16 12 16


The largest commuting value is 47 and the shortest is 1.

** we will round to 8 and in all cases will add 1 if the result is a whole number

ORGANIZING DATA

Next we need to create our classes…

13 47 10 3 16 20 17 40 4 2

7 25 8 21 19 15 3 17 14 6

12 45 1 8 4 16 11 18 23 12

6 2 14 13 7 15 46 12 9 18

34 15 41 28 36 17 24 27 29 9

14 26 10 24 37 31 8 16 12 16

ORGANIZING DATA


13 47 10 3 16 20 17 40 4 2

7 25 8 21 19 15 3 17 14 6

12 45 1 8 4 16 11 18 23 12

6 2 14 13 7 15 46 12 9 18

34 15 41 28 36 17 24 27 29 9

14 26 10 24 37 31 8 16 12 16

Class Limits

1

9

17

25

33

41

Starting with the lowest value, I added the class width of 8 to each class…

ORGANIZING DATA


13 47 10 3 16 20 17 40 4 2

7 25 8 21 19 15 3 17 14 6

12 45 1 8 4 16 11 18 23 12

6 2 14 13 7 15 46 12 9 18

34 15 41 28 36 17 24 27 29 9

14 26 10 24 37 31 8 16 12 16

Class Limits

1 – 8

9 – 16

17 – 24

25 – 32

33 – 40

41 - 48

Starting with the lowest value, I added the class width of 8 to each class…

Now fill in the upper end of each class…notice their difference is 8 as well.

ORGANIZING DATA


13 47 10 3 16 20 17 40 4 2

7 25 8 21 19 15 3 17 14 6

12 45 1 8 4 16 11 18 23 12

6 2 14 13 7 15 46 12 9 18

34 15 41 28 36 17 24 27 29 9

14 26 10 24 37 31 8 16 12 16

Class Limits Tally

1 – 8

9 – 16

17 – 24

25 – 32

33 – 40

41 - 48

We are now going to go thru each data item and place it in its class…

ORGANIZING DATA


13 47 10 3 16 20 17 40 4 2

7 25 8 21 19 15 3 17 14 6

12 45 1 8 4 16 11 18 23 12

6 2 14 13 7 15 46 12 9 18

34 15 41 28 36 17 24 27 29 9

14 26 10 24 37 31 8 16 12 16

Class Limits Tally

1 – 8

9 – 16 I

17 – 24

25 – 32

33 – 40

41 - 48


ORGANIZING DATA


13 47 10 3 16 20 17 40 4 2

7 25 8 21 19 15 3 17 14 6

12 45 1 8 4 16 11 18 23 12

6 2 14 13 7 15 46 12 9 18

34 15 41 28 36 17 24 27 29 9

14 26 10 24 37 31 8 16 12 16

Class Limits Tally

1 – 8

9 – 16 I

17 – 24

25 – 32

33 – 40

41 - 48 I


ORGANIZING DATA


13 47 10 3 16 20 17 40 4 2

7 25 8 21 19 15 3 17 14 6

12 45 1 8 4 16 11 18 23 12

6 2 14 13 7 15 46 12 9 18

34 15 41 28 36 17 24 27 29 9

14 26 10 24 37 31 8 16 12 16

Class Limits Tally

1 – 8

9 – 16 II

17 – 24

25 – 32

33 – 40

41 - 48 I


ORGANIZING DATA


13 47 10 3 16 20 17 40 4 2

7 25 8 21 19 15 3 17 14 6

12 45 1 8 4 16 11 18 23 12

6 2 14 13 7 15 46 12 9 18

34 15 41 28 36 17 24 27 29 9

14 26 10 24 37 31 8 16 12 16

Class Limits Tally

1 – 8 I

9 – 16 II

17 – 24

25 – 32

33 – 40

41 - 48 I


ORGANIZING DATA


13 47 10 3 16 20 17 40 4 2

7 25 8 21 19 15 3 17 14 6

12 45 1 8 4 16 11 18 23 12

6 2 14 13 7 15 46 12 9 18

34 15 41 28 36 17 24 27 29 9

14 26 10 24 37 31 8 16 12 16

Class Limits Tally

1 – 8 I

9 – 16 III

17 – 24

25 – 32

33 – 40

41 - 48 I


ORGANIZING DATA


13 47 10 3 16 20 17 40 4 2

7 25 8 21 19 15 3 17 14 6

12 45 1 8 4 16 11 18 23 12

6 2 14 13 7 15 46 12 9 18

34 15 41 28 36 17 24 27 29 9

14 26 10 24 37 31 8 16 12 16

Class Limits Tally

1 – 8 IIII IIII IIII

9 – 16 IIII IIII IIII IIII I

17 – 24 IIII IIII I

25 – 32 IIII I

33 – 40 IIII

41 - 48 IIII

Continuing that process throughout the entire data list this is the result…

ORGANIZING DATA


13 47 10 3 16 20 17 40 4 2

7 25 8 21 19 15 3 17 14 6

12 45 1 8 4 16 11 18 23 12

6 2 14 13 7 15 46 12 9 18

34 15 41 28 36 17 24 27 29 9

14 26 10 24 37 31 8 16 12 16

Class Limits Tally Frequency

1 – 8 IIII IIII IIII



25 – 32 IIII I

33 – 40 IIII

41 - 48 IIII

Next, we count the tally marks and fill in the frequency in which the data appears in that interval…

ORGANIZING DATA


13 47 10 3 16 20 17 40 4 2

7 25 8 21 19 15 3 17 14 6

12 45 1 8 4 16 11 18 23 12

6 2 14 13 7 15 46 12 9 18

34 15 41 28 36 17 24 27 29 9

14 26 10 24 37 31 8 16 12 16


1 – 8 IIII IIII IIII 14



25 – 32 IIII I

33 – 40 IIII

41 - 48 IIII


ORGANIZING DATA


13 47 10 3 16 20 17 40 4 2

7 25 8 21 19 15 3 17 14 6

12 45 1 8 4 16 11 18 23 12

6 2 14 13 7 15 46 12 9 18

34 15 41 28 36 17 24 27 29 9

14 26 10 24 37 31 8 16 12 16



9 – 16 IIII IIII IIII IIII I 21


25 – 32 IIII I

33 – 40 IIII

41 - 48 IIII


ORGANIZING DATA


13 47 10 3 16 20 17 40 4 2

7 25 8 21 19 15 3 17 14 6

12 45 1 8 4 16 11 18 23 12

6 2 14 13 7 15 46 12 9 18

34 15 41 28 36 17 24 27 29 9

14 26 10 24 37 31 8 16 12 16




17 – 24 IIII IIII I 11

25 – 32 IIII I

33 – 40 IIII

41 - 48 IIII


ORGANIZING DATA


13 47 10 3 16 20 17 40 4 2

7 25 8 21 19 15 3 17 14 6

12 45 1 8 4 16 11 18 23 12

6 2 14 13 7 15 46 12 9 18

34 15 41 28 36 17 24 27 29 9

14 26 10 24 37 31 8 16 12 16





25 – 32 IIII I 6

33 – 40 IIII

41 - 48 IIII


ORGANIZING DATA


13 47 10 3 16 20 17 40 4 2

7 25 8 21 19 15 3 17 14 6

12 45 1 8 4 16 11 18 23 12

6 2 14 13 7 15 46 12 9 18

34 15 41 28 36 17 24 27 29 9

14 26 10 24 37 31 8 16 12 16





25 – 32 IIII I 6

33 – 40 IIII 4

41 - 48 IIII


ORGANIZING DATA


13 47 10 3 16 20 17 40 4 2

7 25 8 21 19 15 3 17 14 6

12 45 1 8 4 16 11 18 23 12

6 2 14 13 7 15 46 12 9 18

34 15 41 28 36 17 24 27 29 9

14 26 10 24 37 31 8 16 12 16





25 – 32 IIII I 6

33 – 40 IIII 4

41 - 48 IIII 4


ORGANIZING DATA


13 47 10 3 16 20 17 40 4 2

7 25 8 21 19 15 3 17 14 6

12 45 1 8 4 16 11 18 23 12

6 2 14 13 7 15 46 12 9 18

34 15 41 28 36 17 24 27 29 9

14 26 10 24 37 31 8 16 12 16

Class Limits Tally Frequency Class Midpt




25 – 32 IIII I 6

33 – 40 IIII 4

41 - 48 IIII 4

The last thing we need to do is calculate the class midpoint…

ORGANIZING DATA


13 47 10 3 16 20 17 40 4 2

7 25 8 21 19 15 3 17 14 6

12 45 1 8 4 16 11 18 23 12

6 2 14 13 7 15 46 12 9 18

34 15 41 28 36 17 24 27 29 9

14 26 10 24 37 31 8 16 12 16


1 – 8 IIII IIII IIII 14 4.5



25 – 32 IIII I 6

33 – 40 IIII 4

41 - 48 IIII 4

𝑚𝑖𝑑𝑝𝑜𝑖𝑛𝑡=8−12

=4.5

ORGANIZING DATA


13 47 10 3 16 20 17 40 4 2

7 25 8 21 19 15 3 17 14 6

12 45 1 8 4 16 11 18 23 12

6 2 14 13 7 15 46 12 9 18

34 15 41 28 36 17 24 27 29 9

14 26 10 24 37 31 8 16 12 16



9 – 16 IIII IIII IIII IIII I 21 12.5


25 – 32 IIII I 6

33 – 40 IIII 4

41 - 48 IIII 4


=12.5

ORGANIZING DATA


13 47 10 3 16 20 17 40 4 2

7 25 8 21 19 15 3 17 14 6

12 45 1 8 4 16 11 18 23 12

6 2 14 13 7 15 46 12 9 18

34 15 41 28 36 17 24 27 29 9

14 26 10 24 37 31 8 16 12 16




17 – 24 IIII IIII I 11 20.5

25 – 32 IIII I 6

33 – 40 IIII 4

41 - 48 IIII 4


=20.5

ORGANIZING DATA


13 47 10 3 16 20 17 40 4 2

7 25 8 21 19 15 3 17 14 6

12 45 1 8 4 16 11 18 23 12

6 2 14 13 7 15 46 12 9 18

34 15 41 28 36 17 24 27 29 9

14 26 10 24 37 31 8 16 12 16




17 – 24 IIII IIII I 11 20.5

25 – 32 IIII I 6 28.5

33 – 40 IIII 4 36.5

41 - 48 IIII 4 44.5

𝐴𝑛𝑑 𝑠𝑜𝑜𝑛…

ORGANIZING DATA




17 – 24 IIII IIII I 11 20.5

25 – 32 IIII I 6 28.5

33 – 40 IIII 4 36.5

41 - 48 IIII 4 44.5

These basic frequency tables only show HOW MUCH data falls into each class. But sometimes we need to know what percentage of data falls into each class. This is called a Relative Frequency

ORGANIZING DATA




17 – 24 IIII IIII I 11 20.5

25 – 32 IIII I 6 28.5

33 – 40 IIII 4 36.5

41 - 48 IIII 4 44.5


OR

ORGANIZING DATA

Class Limits Tally Frequency Class Midpt Rel. Freq.



17 – 24 IIII IIII I 11 20.5

25 – 32 IIII I 6 28.5

33 – 40 IIII 4 36.5

41 - 48 IIII 4 44.5


OR

So let’s add another column to our table…

ORGANIZING DATA




17 – 24 IIII IIII I 11 20.5

25 – 32 IIII I 6 28.5

33 – 40 IIII 4 36.5

41 - 48 IIII 4 44.5


OR


There were 60 data items in our data list…

ORGANIZING DATA


1 – 8 IIII IIII IIII 14 4.5 0.23


17 – 24 IIII IIII I 11 20.5

25 – 32 IIII I 6 28.5

33 – 40 IIII 4 36.5

41 - 48 IIII 4 44.5


OR


𝑓𝑛

=1460

=0.23

ORGANIZING DATA


1 – 8 IIII IIII IIII 14 4.5 0.23

9 – 16 IIII IIII IIII IIII I 21 12.5 0.35

17 – 24 IIII IIII I 11 20.5

25 – 32 IIII I 6 28.5

33 – 40 IIII 4 36.5

41 - 48 IIII 4 44.5


OR


𝑓𝑛

=2160

=0.35

ORGANIZING DATA


1 – 8 IIII IIII IIII 14 4.5 0.23


17 – 24 IIII IIII I 11 20.5 0.18

25 – 32 IIII I 6 28.5

33 – 40 IIII 4 36.5

41 - 48 IIII 4 44.5


OR


𝑓𝑛

=1160

=0.18

ORGANIZING DATA


1 – 8 IIII IIII IIII 14 4.5 0.23


17 – 24 IIII IIII I 11 20.5 0.18

25 – 32 IIII I 6 28.5 0.10

33 – 40 IIII 4 36.5

41 - 48 IIII 4 44.5


OR


𝑓𝑛

=660

=0.10

ORGANIZING DATA


1 – 8 IIII IIII IIII 14 4.5 0.23


17 – 24 IIII IIII I 11 20.5 0.18

25 – 32 IIII I 6 28.5 0.10

33 – 40 IIII 4 36.5 0.07

41 - 48 IIII 4 44.5


OR


𝑓𝑛

=460

=0.07

ORGANIZING DATA


1 – 8 IIII IIII IIII 14 4.5 0.23


17 – 24 IIII IIII I 11 20.5 0.18

25 – 32 IIII I 6 28.5 0.10

33 – 40 IIII 4 36.5 0.07

41 - 48 IIII 4 44.5 0.07


OR


𝑓𝑛

=460

=0.07

once we gather our data we need a way to represent our findings. one way to do this is through the...

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