Pupils - dataset

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.

Final 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

Help us improve! If you spot a mistake, please let let us know. Thank you!

Tips for related online calculators

Looking for help with calculating arithmetic mean?
Looking for a statistical calculator?
Looking for a standard deviation calculator?

statistics

basic operations and concepts

Grade of the word problem

We encourage you to watch this tutorial video on this math problem: video1