Question

what is correct About relative frequency distribution histogram(more can be choosen)

1. the total area of all bars is equal to 1
2. the trial area of all bars is equal to the number of values in a sample
3. the total height of all bars are equal to 1.
4. the height of the bars highly depends on number of bins
5. the height of a bar is a percent values in the corresponding bin divided to its width
6. the height of a bar is a percent of values in corresponding bin.

what is correct about density distribution histogram(can choose several)
1. the total area of all bars are equal to 1
2. the total area of all bars is equal to the number of values in a sample
3. the sum of height of all bars is equal to 1
4. the height of bars highly depends in number of bins
5. the height of a bar is a percent of values in the corresponding bin divided by its width
6. the height of a bar is a percent of values in corresponding bin

Answer 1

A relative frequency histogram is a modified version of frequency histogram. Rather than using vertical axis for the count of data values, relative frequency histogram uses the overall proportion of data values that fall into this bin. Since 100% = 1, all bars must have a height from 0 to 1. Therefore the heights of all of the bars of relative frequency histogram must sum to 1. Therefore total area of the bars is equal to 1.The height of the bar is the percentage of the total number of data values.

The right options are :1,3 ,4 and6.

For a density histogram: draw a rectangle for each class with the class interval as the base and the height equal to

Where the class intervals are (c₀, c₁] , (c₁, c₂] , ...,.

The total area of all bars are equal to 1. The sum of height of all bars is equal to the number of values in a sample. Obviously the height of bar is depends in number of bins. For an example if the bin of 50-60 has a frequency 50. If we change the bin width from 50-55 and 55-60 then the frequency will change as a result height will also change.

Options are 1,2 and 4