Grade Level v.s. Above Grade Level

1
Grade Level v.s. Above Grade Level
Statistically, what does it MEAN?
Emily Vorp Tools for Data Analysis November 1,
2007
2
Background

• Students selected to be in an above-grade-level
  class must meet the following criteria
• Teacher recommendation
• High score on standardized test
• High achieving attitude

3
The Problem

• What is the relationship between grades earned
  by students in a Grade-Level Math Class versus
  grades earned by students in an
  Above-Grade-Level Math Class?

4
Prediction
Since the process for acceptance in the
Above-Level Program is so selective, it would
seem that the students grades in this class
would have a much smaller spread than the
students grades in a corresponding Grade-Level
class.
5
Population

• The data analyzed in the Grade-Level Math Class
  are from a 7th grade math class doing 7th grade
  math.
• The data analyzed in the Above-Grade-Level Math
  Class are from a 6th grade math class doing 7th
  grade math.
• Both classes follow the same curriculum and 90
  of the graded assignments in each class are the
  same.

6
The Data
On-Grade-Level
Above-Grade-Level
7
Descriptive Statistics
On-Grade-Level
Above-Grade-Level
8
Descriptive Statistics
On-Grade-Level
Above-Grade-Level

• The Above-Grade-Level Math Class has a higher
  mean, median, and mode, than the Grade-Level math
  class.
• In an ideal distribution, the median and mean
  should be the same value. The difference between
  the mean and median in the Above-Grade-Level Math
  Class 0.83, while in the Grade-Level Math Class
  it is 3.5.
• The Grade-Level Math Class has a larger range and
  therefore a higher standard deviation.

9
Stem-and-Leaf Plot
Above-Grade-Level v.s. Grade-Level
From this back-to-back stem-and-leaf plot, we see
that both math classes have the majority of
grades clustered in the 80s and 90s.
10
Box Plot Data
11
Outliers?

• Based on the data for the Above-Grade-Level Math
  Class, outliers would be below 84.25 and above
  94.25 . Therefore, there are no outliers.
• Based on the data for the Grade-Level Math Class,
  outliers would be below 67.5 and above 103.5.
  Therefore, 58 is a significant outlier.

12
Box Plot Data
min
min
Q1
Q1
med
med
Q3
Q3
max
max
13
Box Plot
Above-Grade-Level v.s. Grade-Level
On-Grade-Level
Above-Grade-Level
Grade Percentage
In this pictorial representation of the data, it
is clear that the grades of the students in the
Above-Grade-Level Math Class are closely
clustered around the median. The grades of the
students in the Grade-Level Math Class have a
much greater spread.
14
Conclusion
The data that was collected and analyzed in this
investigation, supports the hypothesis that the
grades of the students in an Above-Grade-Level
Math Class have a smaller spread than the grades
of the students in an On-Grade-Level Math Class.