1. ## Question on histogram

Lifespan of bulbs(days)---------Number of bulbs
100< x <=120------------------------15
120< x <=160------------------------105
160< x <=180------------------------130
180< x <=220------------------------230
220< x <=240------------------------20

Question:
When a histogram is drawn to represent this information, the rectangle representing the bulbs with lifespan in the interval 100< x <=120 has width 2 cm and height 3 cm. Find the width and the height of the rectangle representing the bulbs with lifespan in the interval 180< x <=220.

I found this question from a book. the answer given is as follow:
Width
100 < x <=120 (20 units) -> 2 cm
180 < x <=220 (40 units) -> 4 cm

Height
15 bulbs -> 3 cm implies 1 bulb -> 0.2 cm
Thus for 180< x <=220, 230 bulbs -> 46 cm

I understand how to get the width. But I have a question regarding the height.
area of bar for 100<x<=120 is 2*3=6 cm square
6 cm square ->15 units implies 1 cm square -> 2.5 units
So area of bar for 180<x<=220 is 230/2.5=92 cm square
Since the width is 4 cm for the interval 180<x<=220
So the height is 92/4=23 cm!! which is half of the answer above!! I thought when the width of the two intervals are different, then we can't just use the ratio to find the height, there is something to do with the area, right?

Furthermore, from wikipedia I found out that for histogram, the area of each bar has to be equal to the frequency. But obviously this is not true for the question above, right?

I'm quite confused about the concept, like when do we have to make sure that the area of each bar represents the frequency.
Can anyone help me? Urgent!! Test is coming....

2. Originally Posted by acc100jt
...
I'm quite confused about the concept, like when do we have to make sure that the area of each bar represents the frequency.
Can anyone help me? Urgent!! Test is coming....
Hello,

maybe this helps a little bit further: BBC - GCSE Bitesize - Maths | Data handling: higher | Histograms

Click on "Drawing histograms"