If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

## Statistics and probability

### Course: Statistics and probability>Unit 4

Lesson 1: Percentiles

# Analyzing a cumulative relative frequency graph

Find percentiles, median, quartiles, and IQR using a cumulative relative frequency graph.

## Want to join the conversation?

• How did you find the first and third quartile?
• when we look at a data set, we split it into what we call a five number summary: the minimum, the first quartile, the median, third quartile, and maximum.

by looking at it this way, we can see that the first and third quartiles are the values that are directly between the median and the minimum/ maximum (in other words, what is exactly at 25% and 75%).

So, on the graph, we simply find 25% and 75% and write those values, in this case, 18 and 39.
• Where does the name "Cumulative relative frequency" come from, how can it be interpreted?.
I mean what is a good way to think about it in order to remember what is it about?...
• the point say, 50 grams of sugar, will have a y-axis of the number of drinks with at most 50 grams of sugar in them. Though I'm not sure where the relative part comes from
• What does it mean by "cumulative relative frequency"?
• Cumulative relative frequency is the accumulation of the previous relative frequencies. To find the cumulative relative frequencies, add all the previous relative frequencies to the relative frequency for the current row.
• where did you get 25% and 75% from?
• 25% is the first quartile and 75% is the third. You find the IQR by subtracting the first from the third quartile.
• I have a question about a Excel thing we have to draw.. and it is awfully confusing. I am trying to draw a frequency chart. and then a histogram. I can't seem to get it right. The numbers are (a) Construct a frequency distribution for the number of different residences occupied by graduating seniors during their college career:
1, 4, 2, 3, 3, 1, 6, 7, 4, 3, 3, 9, 2, 4, 2, 2, 3, 2, 3, 4, 4, 2, 3, 3, 5.
• How do we fill in a table of cumulative frequency?
• For each unique value in your data, count how many times it appears (frequency), then divide it by total frequency to get relative frequency.
Start filling the table with the frequency of the first value. For the next, add the frequency of the next value to the previous row's cumulative frequency. Repeat this for all values.
(1 vote)
• How do you find the first and third quartile? Plz help.
• Find the median then use the median to split the data into two equal parts with the median separating them.

Now for each of these two parts find the median again. The smaller one is the first quartile and the larger is the third quartile.

Does that make sense? Or would you like a demonstration?
• I don't get Cumulative frequency because in my book it says The Cumulative Freq is the sum of all added up to and including the current one
• Yes, the cumulative frequency of 20 grams of sugar is equal to the number of drinks that contain 20 grams of sugar or less.

To get the cumulative relative frequency of 20 grams of sugar, we divide that number by the total number of drinks, namely 32.

From the graph, we see that the cumulative relative frequency of 20 grams of sugar is approximately 0.3, which means that about 30% of the 32 drinks contained at most 20 grams of sugar.
30% of 32 = 9.6, so 9 or 10 of the drinks contained 20 grams of sugar or less, which is the cumulative frequency of 20 grams of sugar.