Question

Consider the following population of N = 12 scores:

2; 3; 3; 3; 4; 4; 4; 4; 5; 5; 5; 6
(a) Construct a frequency distribution table for the distribution of scores.

Answer 1

Explanation:

1. Find the minimun and maximun value of the data.

Minimun: 2

Maximun: 6

2. Calculate the range (R).

Range=

6 - 2=

4

3. Calculate the average.

Average= (Sum of all values) / N

Average= (2+3+3+3+4+4+4+4+5+5+5+6) / 12

Average= (48) / 12

Average= 4.

4. Calculate the M and round the value down.

`M=√(N) =√(12)=3.46`

`M= 3`

6. Calculate A.

`A=(R)/(M) =(4)/(3) =1.3333`

7. Craft your table.

(Check attatched image 1).

LL: Lower limit.

UL: Upper limit.

8. Calculate the limits and fill out the table.

LL / UL

2.00 2.00+A=3.33

3.33 3.3333 +A=4.66

4.66 5.99

5.99 7.32

7.32 8.65

Filled out table: check attatched image 2.

9. Check the data, count how many values fall into each interval and annotate on "frequency".

For example: There are 4 values between 2 and 3.33, these values are 2,3,3, and 3. Therefore, we write 4 on the frequency (absolute) cell for this row of the table. And we do the same for all the other classes.

Check attatched image 3.

10. Calculate the frequency (relative) for all classes.

For example: the first class (row 1 of the table) contains 4 values. Therefore, it's relative frequency would be:

`(4)/(N)=(4)/(12) =0.3333=`33.33%

Note: We divide by 12 because N=12.

Do the same for all the other rows and finish filling out the table.

Check attatched image 4.

-------------------------------------------------------------------------------------------------------

Extra. To make an histogram, take the interval and the absolute frequency and graph it in the fashion shown in attatched image 5.