Mathematics 9709 · AS & A Level · Sampling and estimation

Sampling and estimation — practice question

The heights, in cm, of the 11 members of the Anvils athletics team and the 11 members of the Brecons swimming team are listed below. Anvils: 173, 158, 180, 196, 175, 165, 170, 169, 181, 184, 172. Brecons: 166, 170, 171, 172, 172, 178, 181, 182, 183, 183, 192.
(i)[4]

Draw a back-to-back stem-and-leaf diagram to show this information, with Anvils on the left-hand side of the diagram and Brecons on the right-hand side.

(ii)[3]

Find the median and the interquartile range of the Anvils' heights.

(iii)[4]

Let $x$ cm denote the heights of the 11 members of the Anvils. You are told that $\sum x = 1923$ and $\sum x^2 = 337221$. Three new members join the Anvils, and their heights are 166 cm, 172 cm and 182 cm. Find the standard deviation of the heights of all 14 members of the Anvils.

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