Grade point average

Question

The grade point averages (GPA) of 20 Second year students selected at random from classes over a two year period are as follows;

2004  2005
3.2    2.7
2.8    3.8
2.5    1.8
3.7    2.0
2.3    2.5
1.9    2.4
2.9    3.0
3.3    2.5
2.8    3.2
2.1    1.9


Can you help me to find out
• Which class had a better grade point average? explain
• Calculate mean, mode and median with values
• Variance and standard deviation for each data set

Answer 1

Either you have been instructed on how to do 1-variable statistics on a calculator (I formerly used TI-84), or your class has provided you with formulas and examples of how to do these calculations by hand).

 

So get to work.  The first question (gpa average, 2004 vs. 2005) is quite easy; add up the column of values for a year, and divide by 20, carrying the gpa value out to 3 decimal places for purposes of comparison).  These two averages are in fact "means" and then you can use the definitions of mode and median, after sorting into ascending values, to answer those questions.

 

Et cetera.  So you have encouragement to work, and learn therefrom.

Answer 2

 

 

• Which class had a better grade point average? explain

 

Add all the students GPA's for the given class year and divide by the number of students.

2004: Class GPA 2.15

2005: Class GPA 2.58

• Calculate mean, mode and median with values

 

The mean is the average class GPA calculated above.

The median is the middle value in all of the numbers listed in numerical order.

The mode is the number that occurs most in a list of numbers.

If no number repeats in the list, then there would be no mode.

 

2004  2005
1.9    1.8
2.1    1.9
2.3    2.0
2.5    2.4
2.8    2.5
2.8    2.5
2.9    2.7
3.2    3.0
3.3    3.7
3.7    3.8

 

2004 Median GPA 2.8

2005 Median GPA 2.5

 

2004 Mode 2.8

2005 Mode 2.5

 

• Variance and standard deviation for each data set

Variance is the average of the squared differences from the Mean. The 2004 class mean GPA was 2.15

2004 variance:

[(2.15-1.9)² + (2.15-2.1)² + (2.15-2.3)² + (2.15-2.5)² + 2*(2.15-2.8)² + (2.15-2.9)² + (2.15-3.2)² + (2.15-3.3)² + (2.15-3.7)² ]/10 

[0.0625+0.0025+0.0225+0.1225+0.845+0.5625+1.1025+1.3225+2.4025]/10 = 6.445/10

= 0.6445

 

The Standard Deviation is a measure of how spread out numbers are. It is the square root of variance

2004 Class Standard deviation:

Sqrt(0.6445) = 0.803