January 2008 - Question 1




The mode can easily be read off by identifying which number occurs the most.
As you can see, it would be 7 (as 0 | 7 represents 7 and this number occurs 3 times).

The median is the middle number when all the numbers are arranged in ascending order.
As the stem and leaf diagram is ordered, we can just count the amount of numbers - in this diagram there are 28.
Then we add 1 to that number and half it - giving us 14.5. We would now find the value which is inbetween the 14th and 15th values - which is 12.5.
So the median would be 12.5.




We can easily get the skewness from the stem and leaf diagram by just drawing a line around the numbers like this:



Then, if we flip our paper round, we can look at it like a graph:



You can see that the data is positively skewed as most values are on the left side.




(A) For this question we should look back at the diagram.
As you can see, we have a large outlier (58). This would affect the mean a lot more than it would effect the median. So for part (A) we would choose the median.

(B) As we explained above, the median would be best because of a large outlier.




This question is a lot easier than it looks. We are going to use 14.75 as an estimate of how many texts each person sends.
As there are 28 people in the class, we need to multiply 14.75 by 28 which gives us 413.
Then we just need to multiply 413 by 0.10 to give us the cost - £41.30

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