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I am confused with the answer given in the A-Level book S1. Please see the following question and please tell me why answer is 38 and not 24. Is it misprinting or am I missing out something?

Question: The nurse at a health centre records the heights, h cm, to the nearest cm, of a group of boys in the same school age group. The frequency table shows the result

\begin{array}{|c|c|c|} \hline h& Frequency & Cumulative freqency \\ \hline 165& 8& 8&\\ \hline 166& 7& 15&\\ \hline 167& 9& 24&\\ \hline 168& 14& 38&\\ \hline 169& 18& 56&\\ \hline 170& 16& 72&\\ \hline \end{array}.

State the number of boys who are less than 168 cm tall.

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    I would have suggested $31$: all those rounded to $167$ or below plus (about) half those rounded to $168$2012-12-30

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Less than $168$ presumably includes numbers like $167.92$. Since $168$ (exactly) is unlikely, the answer $38$ is substantially more reasonable than $24$. Less than $168$ does not mean $167$ or below.

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    As entries in col$u$mn h are rounded to nearest cm, so you are treating entries in column h as 'class' with class boundary 167.5-168.5 for fourth entry (which is 168). Is that right? If that's so then it makes a 'bit' sense. Though still what if some boys height is 168.3. That boy is included in this class. So it doesn't make complete sense as answer is quite dodgy.2012-12-29