Thirty-six runners finished a 100 m race in the times shown…

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Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

Thirty-six runners finished a $100\ \text{m}$ race in the times shown.

Time (seconds)	Runners
12-14	4
14-16	9
16-18	12
18-20	7
20-22	4

Find the mean time by the assumed mean method with $a = 17$ .

Need a reminder? The key ideaShow

Measure the class marks from an assumed mean $a$ . The deviation is $d = x - a$ and

\displaystyle \bar{x} = a + \dfrac{\sum fd}{\sum f}.

Any $a$ gives the same mean. A change of $a$ changes $\sum fd$ by $N$ times the change of $a$ .

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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