Histogram of unequal class width

[kelvin macks]

for the class 100-199, the f (number of household) is 20, but in the histogram, the frequency is divided by 2 which 20/2 = 10 , but how can it show that in the class 100-199 , the total frequency of 100-199 is 10 ? when i look at the histogram, i would directly think that there are f=10 in the class of 100-199... how can it relate to the f for 100-199 is 20? i totally can't undrestand.

 

[DrClaude]

Imagine that you had $f=10$ for class 100-149 and $f=10$ for class 150-199, what would the bar graph look like? Now imagine that the some of the information is lost, and you only know that $f=20$ for class 100-199. Why should the graph then be different? (Note that I split it into two times 10 for illustration purposes. In reality, this is only true on average. Increasing the class size means that the average is taken over a greater interval.)

What is important is the area of the bar in the graph.

 

[kelvin macks]

Imagine that you had $f=10$ for class 100-149 and $f=10$ for class 150-199, what would the bar graph look like? Now imagine that the some of the information is lost, and you only know that $f=20$ for class 100-199. Why should the graph then be different? (Note that I split it into two times 10 for illustration purposes. In reality, this is only true on average. Increasing the class size means that the average is taken over a greater interval.)

What is important is the area of the bar in the graph.

i can understand your explanation. why can't i just draw f=20 for 100-199? since the question only give f=20 for 100-199

 

[kelvin macks]

shall i label the y-axis of the graph above as frequency density?

 

[DrClaude]

i can understand your explanation. why can't i just draw f=20 for 100-199? since the question only give f=20 for 100-199

Because you have to normalize the data to take into account the class width. The total area must be the same whatever you choose as the size of the bins.

Say there is no household that consumed less than 100 kWh. You could then make the class go from 0 to 199, and you would still have $f = 20$. Do you still think that the bar should go up to 20 from 0 to 199?

 

[DrClaude]

shall i label the y-axis of the graph above as frequency density?

I'm not sure if it's appropriate to call it that. I'll leave it to others to answer that.

It is true that the y scaling would change if the original data had been binned in smaller bins. Here, the data is normalized to what they call the "standard width."