Check your next statistical test with this helpful guide
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Histograms or frequency distributions are statistical graphs that show how often a particular value is observed in a data set. To find the median or mean of a histogram, add up all the values in your data set, then add 1 and divide the result by 2. If you’re struggling with your statistics homework, keep reading for more detailed equations, plus tips on how to understand them.
- Add up all the frequencies in the histogram. If you don’t have the frequencies yet, multiply the range of x values of each bar by their y value (height).
- If the value is odd, add 1 and divide by 2 to get the median. The equation is n+1/2 where n is equal to the total value of the frequencies.
- If the value is even, find the average of the two middle numbers. The equation is n/2+(n/2+1)/2
Determine the values of each bar on the histogram. If your problem doesn’t give you the total value of a given “bin” (x-axis range, eg 1-5) of the histogram, multiply the bin by the value on the y-axis.[1]
- For example, if you have a bin with a range of 15 (1-15, 15-30, etc.) with a y-axis value of 20, the total value of that bin would be 15×20=300.
- Usually, the bins on a histogram are uniform (all 15 widths, for example), but if you’re working on homework, your teacher may make different ranges of bins to make the task more difficult.[2]
- For example, you can have a container with a range of 20 and another with a range of 25.
- Consider entering your values into a frequency table. Frequency tables have two columns, one with the values and one with the number of times that value was recorded.[3]
So if the value “1” was recorded 7 times and the value “2” was recorded 3 times, then the first row of the table would be 1.7 and the second would be 2.3.
Add up all the frequencies. Once you have the value of each bin, add them all together to get the total frequency value on the graph.[4]
- So if you have 3 bins with ranges of 15, one with an ay value of 20, one with an ay value of 30, and one with an ay value of 40, the total value of the frequencies on the graph would be (15×20) + (15×30) + (15×40) = 1350.
- The sum of the frequencies is also the total area of the graph.
If the value is odd, add 1 to the total value, then divide by two. In mathematical notation, the equation looks like n+1/2.[5]
The median is the exact middle of the data set, that is, the value of a number equidistant from 1 to the total sum- For example, 3 is the median of a data set with a summed value of 5: 5+1/2 = 3, 1, 2, 34, 5.
If the value is even, take the average of the two middle numbers. Since even numbers do not have an exact middle, divide the number by 2, then find the average of that number and the next number.[6]
In mathematical notation, the equation is n/2+(n/2+1)/2.- So if your total is 10, you would find the median by adding 5 to n/2 and 6 to n/2 + 1. 10/2+(10/2+1)/2 = 5+6/2 = 5.5.
Estimate the exact value using the equation L + (n/2 – F/f)w. Let L = lower limit of the range in which the median falls, n = sum of all frequencies on the histogram, F = sum of all frequencies up to the middle range, f = y value of the middle range, iw = range of x values of the middle space.[7]
F represents the cumulative frequency. Calculate the cumulative frequency by adding the total values of each bin up to the bin in which the median falls. So if your median is in the “30-40” bin, and your chart starts at zero, add the total values of the 0-10 , 10-20 , and 20-30 bins.
- If the total value of your histogram was 180, your median bin had an x-value of 30-40 and an ay-value of 35, and the cumulative frequency up to that bin was 60, then your equation would look like (30+180/2 – 60/ 35)10 = (30+90 – 60/35)10 = (30+30/35)10 = (30+0.857)10 = 38.57.
- The result of this equation is a value on the x-axis that has equal areas on both sides. So the area of the graph on the left is equal to the area of the graph on the right of the value.[8]
Add all the values in the histogram. Multiply the width of each bin by the height (the range of each bar on the x-axis by the value on the y-axis). [9]
Then add them all together. This is the same as calculating the area of a graph.Divide the sum of the values by the number of data points. To find the average value on the graph, divide the total from the last step by the number of values recorded.[10]
So if you have a graph with 15 data points that add up to 300, then the mean would be 300/15 = 20.- It may help to make a frequency table. To make a table, write all the values that are recorded in one column, then write the number of times each given value is recorded in the next column.[11]
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Source: HIS Education