Statistical Methods for Psychology

together into a histogram.^1 Our goal in doing so would be to obscure some of the random

“noise” that is not likely to be meaningful, but preserve important trends in the data. We

might, for example, group the data into blocks of 5/100 of a second, combining the frequen-

cies for all outcomes between 35 and 39, between 40 and 44, and so on. An example of such

a distribution is shown in Table 2.3.

In Table 2.3, I have reported the upper and lower boundaries of the intervals as whole

integers, for the simple reason that it makes the table easier to read. However, you should

realize that the true limits of the interval (known as the real lower limit and the real upper

limit) are decimal values that fall halfway between the top of one interval and the bottom

of the next. The real lower limitof an interval is the smallest value that would be classed

as falling into the interval. Similarly, an interval’s real upper limitis the largest value that

Section 2.2 Histograms 19

(^1) Different people seem to mean different things when they talk about a “histogram.” Some use it for the distribution
of the data regardless of whether or not categories have been combined (they would call Figure 2.1 a histogram), and
others reserve it for the case where adjacent categories are combined. You can probably tell by now that I am not a
stickler for such distinctions, and I will use “histogram” and “frequency distribution” more or less interchangeably.
15
0
35 55 75 95 115
Frequency
Reaction time (Hundredths of a second)
12
9
6
3
Figure 2.1 Plot of reaction times against frequency
real lower limit
real upper limit
histogram
Table 2.3 Grouped frequency distribution
Cumulative Cumulative
Interval Midpoint Frequency Frequency Interval Midpoint Frequency Frequency
35–39 37 7 7 85–89 87 4 291
40–44 42 20 27 90–94 92 3 294
45–49 47 35 62 95–99 97 3 297
50–54 52 41 103 100–104 102 2 299
55–59 57 47 150 105–109 107 0 299
60–64 62 54 204 110–114 112 0 299
65–69 67 39 243 115–119 117 0 299
70–74 72 22 265 120–124 122 0 299
75–79 77 13 278 125–129 127 1 300
80–84 82 9 287