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