152 Proceedings of the Royal Society of Edinburgh. [Sess. 
Table I. — Average Mark gained by a Boy aged x Years and y Months 
at October 1 , 1920. 
The marks have been smoothed in sets of three months. Column 3 gives the number 
of boys of each age, and column 4 the number in each set of three months. 
(1) 
Age. 
(2) 
S 
r ce 
-4-3 
c 
EH 
(3) 
to 
O 
PQ 
~o 
6 
£ 
No in Group. 
Average Mark. ^ 
(1) 
Age. 
(2) 
M 
fH 
03 
IS 
O 
EH 
(3) 
CO 
O 
PQ 
'o 
o’ 
No. in Group 
Average Mark. ^ 
(1) 
Age. 
(2). 
fH 
o3 
S 
- 1-3 
O 
EH 
(3) 
02 
>* 
O 
PQ 
O 
6 
£ 
(4) 
o 
u 
0 
o 
Average Mark. ^ 
x y 
X 
V 
X 
y 
10 5 
171 
3 
... 
12 
10 
403 
5 
12 
93 
15 
3 
904 
8 
16 
112 
6 
275 
4 
9 
62 
11 
548 
5 
16 
91 
4 
588 
5 
20 
110 
7 
115 
2 
7 
63 
13 
0 
500 
6 
16 
96 
5 
713 
7 
18 
114 
8 
52 
1 
3 
57 
1 
487 
5 
12 
90 
6 
765 
6 
17 
118 
9 
4 
57 
2 
93 
1 
18 
93 
7 
521 
4 
13 
125 
10 
175 
3 
8 
56 
3 
1094 
12 
20 
93 
8 
337 
3 
9 
116 
11 
285 
5 
10 
54 
4 
670 
7 
24 
94 
9 
197 
2 
11 
109 
11 0 
78 
2 
9 
56 
5 
499 
5 
15 
96 
10 
661 
6 
10 
110 
1 
147 
2 
8 
61 
6 
275 
3 
13 
95 
11 
243 
2 
10 
113 
2 
262 
4 
8 
64 
7 
457 
5 
14 
95 
16 
0 
228 
2 
13 
136 
3 
111 
2 
12 
66 
8 
605 
6 
19 
103 
1 
1293 
9 
14 
131 
4 
423 
6 
10 
76 
9 
899 
8 
18 
112 
2 
320 
3 
15 
131 
5 
228 
2 
15 
74 
10 
519 
4 
16 
116 
3 
350 
3 
9 
110 
6 
444 
7 
13 
70 
11 
440 
4 
15 
116 
4 
316 
3 
10 
119 
7 
240 
4 
14 
66 
14 
0 
784 
7 
19 
110 
5 
522 
4 
13 
130 
8 
246 
3 
11 
74 
1 
865 
8 
19 
110 
6 
853 
6 
14 
138 
9 
321 
4 
11 
81 
2 
447 
4 
16 
106 
7 
551 
4 
11 
133 
10 
324 
4 
14 
77 
3 
389 
4 
12 
100 
8 
81 
1 
7 
128 
11 
438 
6 
17 
88 
4 
368 
4 
10 
96 
9 
266 
2 
3 
122 
12 0 
625 
7 
14 
88 
5 
202 
2 
11 
96 
10 
4 
147 
1 
78 
1 
14 
77 
6 
388 
5 
12 
93 
11 
321 
*2 
5 
134 
2 
380 
6 
14 
73 
7 
534 
5 
16 
104 
17 
0 
350 
3 
12 
129 
3 
568 
7 
21 
76 
8 
722 
6 
17 
118 
1 
880 
7 
14 
126 
4 
640 
8 
19 
75 
9 
743 
6 
13 
122 
2 
547 
4 
13 
128 
5 
217 
4 
20 
69 
10 
118 
1 
9 
123 
3 
244 
2 
8 
134 
6 
520 
8 
18 
74 
11 
251 
2 
11 
113 
4 
282 
2 
6 
139 
7 
595 
6 
18 
81 
15 
0 
874 
8 
16 
118 
5 
311 
2 
6 
157 
8 
337 
4 
12 
92 
1 
768 
6 
17 
114 
6 
348 
2 
4 
162 
9 
169 
2 
11 
83 
2 
295 
3 
17 
116 
(7) At the right hand of Table II. is also given the average mark of 
boys of a definite yearly age and the number of boys in each yearly group. 
(a) Marks for ages 12, 13, 14, and 15 may be taken as fairly reliable. 
( b ) The differences between these suggest a parabolic form as very 
suitable for the normal curve. 
(c) The highest mark (140) on this supposition would correspond well 
with many of the averages of Yoakum and Yerkes. In par- 
ticular, it is nearly identical with that given for the 15,385 
cases of the “ White Officers’ Principal Sampling ” (139). 
