Table 11.3 Frequency Table
Cumulative
Class Class Relative Cumulative Relative
Interval Midpoint Tallies Frequency Frequency Frequency Frequency
71-77 74 / 1 2001 = 0. 005 1 0.005
78-84 81 0 2000 = 0. 000 1 0.005
85-91 88 //// 4 2004 = 0. 020 5 0.025
92-98 95 ///// / 6 2006 = 0. 030 11 0.055
98-105 102 ///// ///// / 11 20011 = 0. 055 22 0.110
106-112 109 ///// //// 9 2009 = 0. 045 31 0.155
113-119 116 ///// ///// //////// ///// 23 20023 = 0. 115 54 0.270
120-126 123 ///// ///// //////// ///// 23 20023 = 0. 115 77 0.385
128-133 130 ///// ///// ////////// ///// / 26 20026 = 0. 130 103 0.515
134-140 137 ///// ///// ////////// ///// 25 20025 = 0. 125 128 0.640
141-147 144 ///// ///// ///////// ///// 24 20024 = 0. 120 152 0.760
148-154 151 ///// ////////// /// 18 20018 = 0. 090 170 0.850
155-161 158 ///// ///////// 14 20014 = 0. 070 184 0.920
162-168 165 ///// ///// 10 20010 = 0. 050 194 0.970
168-175 172 /// 3 2003 = 0. 015 197 0.985
176-182 179 / 1 2001 = 0. 005 198 0.990
183-189 186 // 2 2002 = 0. 010 200 1.00
A graphical representation of the data in table 11.3 can be presented by defining
a relative frequency function f(x)and a cumulative relative frequency function F(x)
associated with the sample. These functions are defined
f(x) =
{f
j when x=Xj
0 otherwise
F(x) =
∑
xj≤x
f(xj) = sum of all f(xj)for which xj≤x
(11.1)
and are illustrated in the figure 11-3.
