The question is from an edexcel non-calculator paper...

And the question is number 15.

From the graph, the min and max weights are 160 and 190 grams.
But the next page says its 153 and 186 grams,
So I'm confused as to where the median and upper and lower quartiles should actually be.

Can anyone help, I'm not too sure, thanks.

Hey colin271828.

It is a subtle thing, but if you look at the graph you'll notice that the cumulative frequency graphic doesn't start at 0 but instead starts at 6 with x = 160 so there are some values less than 160, but they are not that likely).

With regards to the maximum, I agree that this does not make any sense. The only way that I can interpret what happened is that the graph is an approximation, but I think this doesn't really cut it if this is the case.

The minimum makes sense, but I agree with you that the maximum makes no sense since there are 60 tomatoes which means the 190g weight is the maximum given that graph.

And have come up with this idea...

Typically data is grouped, so the graph could be drawn from a table such as:

Weight Frequency Cum. Frequency
----------------------------------------------
150<=x<=160 15 15
160 < x<=170 12 27
170 < x<=180 14 41
180 < x<=190 19 60
----------------------------------------------

So if the full ogive was drawn, it would touch the x-axis
so for part a) The median is the middle value from the 61 values (0...60)
So that would be the 31st value, which is 30, which is 170g

For part b), we have a maximum of 186, which is now consistent with the curve,
since we just know 19 values are in the 180-190 interval, we don't actually have to have a value at 190.

And the minimum of 153, fits in as well, ist just the curve for 150-160 isn't shown.

So for the box plot, we have the max and min, 153 and 186.
The lower quartile would be at frequency 15, which is 165
and upper at 45 which is 175, which allows you to draw the box plot.

This seems straightforward now, any thoughts?

Sounds good.

60 tomatoes weighted but 5 lightest ones are ignored, therefore we have 60-6=54 samples and its mid-point is: 6+54/2=33. At 33 cum freq we read wt=172g which is the sought median: half tomatoes larger and half smaller than 172g. Notice that we do this because if the 5 lightest tomatoes weights were included then the resulting graph could have a shift to right or left changing everything.

### cumulative frequency graph doesn't touch x axis

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