Finding averages from a cumulative frequency A cumulative frequency diagram is a good way to represent data to find the median , which is the middle value. The middle of these 40 values is the 20th value, so go across from this value and find the median length. So we’re gonna ignore the median here and just look at these first four numbers and so out of these first four numbers, since I have an even number of numbers, I’m gonna calculate the median using the middle two numbers so I’m gonna look at the middle two numbers here and I’m gonna take their average. A high value for the interquartile range shows that the data is spread out. The interquartile range is another measure of spread, except that it has the added advantage of not being affected by large outlying values. So the upper quartile UQ is I have the middle of the second half,

So the median is going to be To find the upper quartile, find of 40, which is the 30th value. So this is just representing the data in a different way but we could write this again as an ordered list so let’s do that. I have an even number of numbers so to calculate the median, I’m gonna have to look at the middle two numbers. So we’re gonna ignore the median here and just look at these first four numbers and so out of these first four numbers, since I have an even number of numbers, I’m gonna calculate the median using the middle two numbers so I’m gonna look at the middle two numbers here and I’m gonna take their average. I have an odd number of numbers here and it’s going to be the number that has four to the left and four to the right and that middle number, the median is going to be

Firstly there are 11 numbers present. To find the upper quartile, find of 40, which is the 30th value. Video transcript – [Instructor] Let’s get some practice calculating interquartile ranges and Rangw taken some exercises from the Khan Academy exercises here. You can imagine it right over there and then the middle of the second half I’m gonna have to do the same thing.

So 10, 10, 10 then we have an Finding the interquartile range A cumulative frequency diagram is also a good way to find the interquartile rangewhich is the difference between the upper quartile and lower quartile.

I have an odd number of numbers here and it’s going to be the number that has four to the left and four to the right and that middle number, the median is eatch to be Find the interquartile range of the data in the dot plot below.

### Interquartile range (IQR) (video) | Khan Academy

What is the interquartile range of the following data? Well, if you have five numbers, if you have an odd number of numbers, you’re gonna have one middle number and it’s going to intterquartile the one that has interquartlie on either sides. A high value for the interquartile range shows that the data is spread out.

A cumulative frequency mmaths is drawn by plotting the upper class boundary with the cumulative frequency. So let’s do that. It’s going to be the average of these two numbers.

I have the middle of the second half, Length cm Frequency Cumulative frequency 4 4 10 14 11 25 12 37 3 40 A cumulative frequency diagram is drawn by plotting the upper class boundary with the cumulative frequency.

So the middle of the first half is five. The middle of the second eange minus the middle of the first half which is going to be equal to eight. Let’s do some more of these. Interquartile range is just going to be the median of the second half, 12 minus the median of the first half, nine which is going to be equal to three.

I have the middle of the first half is five. The upper class boundaries for warch table are 35, 40, 45, 50 and If you took 12 plus 14 over two, that’s going to be 26 over two which is equal to 13 but an easier way for numbers like this, you say hey, 13 is right exactly halfway between 12 and The value the upper quartile is the median of the upper half of the data.

The middle of these 40 values is the 20th value, so go across from this value and find the median length. The lower quartile is the value at the first quarter once your data has been put in order.

I have one, two, three, four, five, six, seven, eight, nine numbers so there’s going to be just one middle number. So the upper quartile UQ is This has two to the left and it has two to the right. Rrange cumulative frequency diagram creates a running total of the amounts within a table.

## Interquartile range (IQR)

The middle two numbers are 12 and Mean and standard deviation versus median and IQR. Reading from the graph, the upper quartile is I’m just gonna solve it on my scratch pad. You have two to the left and two to the right so the median of the second half is So the lower quartile LQ is 4. We read the values for the quartiles from the graph and arrive at 38 and There interqkartile 7 pieces of ranye, so: We have an A low value for the interquartile range means the data is closer together or more consistent.

So the median is going to be You are allowed to be out by a little but be as accurate as you can. However, it would have had a massive effect on a normal range. No fives interquarfile there is a six.

So all I did here is I wrote this data like this so we could see, okay, this album has seven songs, this album has nine, this album has nine and the way I wrote interquarrile, it’s already in order so I could immediately get, I can immediately start ramge the median. So this is just representing the data in a different way but we could write this again as an ordered list so let’s do that. It is more reliable than the range because it does not include extreme values.

Sort the data from least to greatest and then find the interquartile range of the data set and I encourage you to do this before I take a shot at it. Reading from the graph, the lower quartile is The interquartile range is the difference between the lower quartile and the upper quartile. Songs on each album in Shane’s collection and so let’s see what’s going on here and like always, I encourage you to take a shot at it.