|Av. =4| |Sum x^2 =28|Av. = 8 | |Sum y^2= 112| ============================================================
===

Sum x.y                 +50
r= --------------------------  = ---- = +.89.
sqrt(Sum x^2)sqrt(Sum y^2)     56

Other illustrations might be given to show how the coefficient varies from + 1, the measure of the highest positive relationship (going together) through 0 to -1, the measure of the largest negative relationship (opposition).  A relationship between traits which we measure as high as +.50 is to be thought of as quite significant.  It is seldom that we get a positive relationship as large as +.50 when we correlate the achievements of children in school work.  A relationship measured by a coefficient of +-.15 may not be considered to indicate any considerable positive or negative relationship.  The fact that relationships among the achievements of children in school subjects vary from +.20 to +.60 is a clear indication of the fact that abilities of children are variable, or, in other words, achievement in one subject does not carry with it an exactly corresponding great or little achievement in another subject.  That there is some positive relationship, i.e., that able pupils tend on the whole to show all-round ability and the less able or weak in one subject tend to show similar lack of strength in other subjects, is also indicated by these positive coefficients.

QUESTIONS

1.  Calculate the median point in the following distribution of eighth-grade composition scores on the Hillegas scale.

Quality   0  18  26  37  47  58  67
Frequency         2  68  73   3

2.  Calculate the median point in the following distribution of third-grade scores on the Woody subtraction scale.

    No. problems 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
    Frequency 2 2 2 3 3 5 4 5 8 16 16 16 23 20 21 11 22 11 2

    22 23 24 +
     1

3.  Compare statistically the achievements of the children in two eighth-grade classes whose scores on the Courtis addition tests were as follows: 

    Class A—­6, 5, 8, 9, 7, 10, 13, 4, 8, 7, 8, 7, 6, 8, 15, 6, 7, 0, 6, 9,
    5, 8, 7, 10, 8, 4, 7, 8, 6, 9, 5, 7, 2, 6, 8, 5, 7, 8, 7, 8, 5, 8, 10,
    6, 3, 6, 8, 17, 5, 7.

Class B—­10, 4, 8, 13, 11, 9, 8, 10, 7, 9, 11, 10, 18, 7, 12, 9, 10, 8, 11, 10, 12, 9, 2, 11, 8, 10, 9, 14, 11, 7, 10, 12, 10, 6, 11, 8, 10, 9, 10, 17, 8, 11, 9, 7, 9, 11, 8, 12, 9, 13.

4.  If the marks received in algebra and in geometry by a group of high school pupils were as given below, what relationship is indicated by the coefficient of correlation?

|GEOMETRY |ALGEBRA
|MARKS    |MARKS
1.   |80       |60
2.   |68       |73
3.   |65       |80
4.   |96       |80
5.   |59       |62
6.   |75       |65
7.   |90       |75
8.   |86       |90