S1 Maths

A superstore records the number of hours over time worked by their employees in one particular week. The results are shown in the table.

N F CF
0 25 25
1 10 35
2 20 55
3 10 65
4 25 90
5 10 100

b) Find Q1 and Q3.

c) Work out the interquartile range.

On the answer page Q1 is is 0.5 and Q3 is 4. I understand why Q3 is 4 but not how Q1 is 0.5.

Because time is a continuous measure

So 0 is actually between 0 and 0.5
And 3 is actually between 2.5 and 3.5

there are 50 workers below the median, 50 above.

you can say that the LQ is the median of the 50 below, and the UQ is the median of the 50 above.

so the middle of 50 workers is (50 + 1)/2 = 25.5 thus we need to look at the hours worked by the 25th and 26th workers.

They have worked 0 and 1 hours respectively so we say 0.5

Some books say (100 + 1) *.25 to find the location of the LQ... this gets 25.25 which again is between the 25th and 26th values. You could argue that it is 1/4 of the way between 0 and 1 but to get your answer you need to do 1/2 way

Why isn't Q3 3.5?

101/4 = 25.25

So you need 100-25.25 th person

Personally I think that Q3 is 3.9 but it would not be 3.5 as it is not at the start of that group