Corresponding 33321

The following data on the height and the corresponding number of pupils were found in the measurement of 63 pupils:

a) determine the arithmetic mean
b) determine the median mode
c) determine the variance.
d) represent the data using a polygon.

Correct answer:

m = 170.8095 cm
mod = 173
median = 171
r = 21.8685

n = 1 + 1 + 2 + 1 + 2 + 2 + 3 + 2 + 4 + 3 + 5 + 6 + 7 + 9 + 5 + 2 + 1 + 4 + 2 + 1 = 63 s = 159 \cdot 1 + 161 \cdot 1 + 162 \cdot 2 + 163 \cdot 1 + 164 \cdot 2 + 165 \cdot 2 + 166 \cdot 3 + 167 \cdot 2 + 168 \cdot 4 + 169 \cdot 3 + 170 \cdot 5 + 171 \cdot 6 + 172 \cdot 7 + 173 \cdot 9 + 174 \cdot 5 + 175 \cdot 2 + 177 \cdot 1 + 178 \cdot 4 + 179 \cdot 2 + 181 \cdot 1 = 10761 m = \frac{s}{n} = \frac{1 0 7 6 1}{6 3} = 170.8095 cm

(159, 161, 162, 162, 163, 164, 164, 165, 165, 166, 166, 166, 167, 167, 168, 168, 168, 168, 169, 169, 169, 170, 170, 170, 170, 170, 171, 171, 171, 171, 171, 171, 172, 172, 172, 172, 172, 172, 172, 173, 173, 173, 173, 173, 173, 173, 173, 173, 174, 174, 174, 174, 174, 175, 175, 177, 178, 178, 178, 178, 179, 179, 181) n (173) = 9 \dots m a x m o d = m o d = 173

i = 63 / 2 = \frac{6 3}{2} = 31 \frac{1}{2} = 31.5 m e d i a n = 171

s_{2} = (159 - m)^{2} \cdot 1 + (161 - m)^{2} \cdot 1 + (162 - m)^{2} \cdot 2 + (163 - m)^{2} \cdot 1 + (164 - m)^{2} \cdot 2 + (165 - m)^{2} \cdot 2 + (166 - m)^{2} \cdot 3 + (167 - m)^{2} \cdot 2 + (168 - m)^{2} \cdot 4 + (169 - m)^{2} \cdot 3 + (170 - m)^{2} \cdot 5 + (171 - m)^{2} \cdot 6 + (172 - m)^{2} \cdot 7 + (173 - m)^{2} \cdot 9 + (174 - m)^{2} \cdot 5 + (175 - m)^{2} \cdot 2 + (177 - m)^{2} \cdot 1 + (178 - m)^{2} \cdot 4 + (179 - m)^{2} \cdot 2 + (181 - m)^{2} \cdot 1 = (159 - 170.8095)^{2} \cdot 1 + (161 - 170.8095)^{2} \cdot 1 + (162 - 170.8095)^{2} \cdot 2 + (163 - 170.8095)^{2} \cdot 1 + (164 - 170.8095)^{2} \cdot 2 + (165 - 170.8095)^{2} \cdot 2 + (166 - 170.8095)^{2} \cdot 3 + (167 - 170.8095)^{2} \cdot 2 + (168 - 170.8095)^{2} \cdot 4 + (169 - 170.8095)^{2} \cdot 3 + (170 - 170.8095)^{2} \cdot 5 + (171 - 170.8095)^{2} \cdot 6 + (172 - 170.8095)^{2} \cdot 7 + (173 - 170.8095)^{2} \cdot 9 + (174 - 170.8095)^{2} \cdot 5 + (175 - 170.8095)^{2} \cdot 2 + (177 - 170.8095)^{2} \cdot 1 + (178 - 170.8095)^{2} \cdot 4 + (179 - 170.8095)^{2} \cdot 2 + (181 - 170.8095)^{2} \cdot 1 = \frac{9 6 4 4}{7} = 1377 \frac{5}{7} ≐ 1377.7143 r = s_{2} / n = 1377.7143 / 63 = 21.8685

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