# Frequency table in A-Level Statistic book S1

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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Usually, "less than" implies "less than but not equal to". Otherwise, the explicit "less than or equal to" is used. –  Alfonso Fernandez Dec 29 '12 at 0:02
so answer is 8 + 7 + 9 = 24. but book gives answer 38. So I am right to say that 24 boys have height less than 168cm. –  user18096 Dec 29 '12 at 0:03
Oh, I read it wrong... If the book included 168, then either the book is wrong, or the conventions in the A-levels (they're British, right?) are different. Are you sure the original wasn't "at most 168cm" or something like that? –  Alfonso Fernandez Dec 29 '12 at 0:14
No I have copied exactly what is written in A-level (yes, they're British) book. I am pretty sure it is misprinting as it doesn't make sense to me. I just wanted to double-check. –  user18096 Dec 29 '12 at 0:18
I would still check other places in the book or ask a teacher to make sure this is not used consistently, but you're most probably fine. Good luck with you A-levels! –  Alfonso Fernandez Dec 29 '12 at 0:22

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.