Forty buses ran the distances in the table below…

Contributed by StemPy Lab

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

Forty buses ran the distances in the table below.

Distance (km)	Buses
300-350	5
350-400	9
400-450	14
450-500	8
500-550	4

Mina chose the assumed mean $a = 425\ \text{km}$ and found $\sum fd = -150$ . Her friend Tomas chose $a = 475\ \text{km}$ for the same table.

What does Tomas find for $\sum fd$ , without making a new table?

What mean does he get?

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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