Draw a box-and-whisker plot for each set of data. Magnitude of Recents MajorEarthquakes

step 1 So I'm going to put these numbers in order. Now, when I look at this chart, I notice that there

Draw a box-and-whisker plot for each set of data. ...

Key Concepts

Outliers

Outliers are data points that fall significantly outside the overall pattern of a dataset. In a box-and-whisker plot, outliers are often identified as points that lie beyond the whiskers, which typically extend 1.5 times the interquartile range (IQR) from the quartiles. Recognizing outliers is important as they can affect statistical analyses and interpretations.

Box-and-Whisker Plot

A box-and-whisker plot is a graphical representation used in descriptive statistics that visualizes the distribution of a dataset. It shows the minimum, first quartile, median, third quartile, and maximum values, providing a clear summary of the data's dispersion and central tendency.

Five-Number Summary

The five-number summary is a set of descriptive statistics that includes the minimum, first quartile (Q1), median, third quartile (Q3), and maximum values of a dataset. This summary forms the basis for constructing a box-and-whisker plot and provides insights into the distribution and spread of the data.

Median

The median is a measure of central tendency that represents the middle value of an ordered dataset. It divides the data into two equal halves, with an equal number of observations above and below it, thereby providing a robust indication of the dataset's center.

Quartiles

Quartiles are values that divide a dataset into four equal parts after it has been sorted in ascending order. The first quartile (Q1) marks the 25th percentile, while the third quartile (Q3) marks the 75th percentile. These values help in understanding the spread and concentration of data points, particularly in the middle 50% of the distribution.

Transcript

00:01 So i'm going to put these numbers in order.

00:02 Now, when i look at this chart, i notice that there are 21 data points.

00:06 So i'm going to be very detailed about how i list this out.

00:10 If there are 21, that means there are 10 numbers, and they're going to be 6 .1, 6 .5, 6 .6, 6 .6, 6 .7, 6 .8.

00:33 And 6 .8, those are the first 10 numbers that i come to, which means that that 11th number, because there are 21 data points, that 11th number, which is also 6 .8, i know that's my median, and so i'm just going to put it here in the middle.

00:50 I know i don't have enough room to write these all the way out, so trying to be very conscientious about how i write them.

00:56 The bottom, then, the next 10 after that are going to be 6 .9, 6 .9, 7 .0.

01:03 7 .1, 7 .1, 7 .1, 7 .2, 8 .1, 8 .7 and 9 .0.

01:20 So i know the median.

01:22 I can find my quartiles because now i have 10 numbers on either side of this median number.

01:28 And so my quartiles then are going to fall right in here and right in here.

01:35 And so what i know then is that my lower cord tiles, is 6 .65 and my upper quartile is 7 .1.

01:49 Now when i look at that, there's not a lot of difference between my lower quartile and my smallest number.

01:56 But there is quite a bit of difference here between my upper and my biggest number.

02:01 So i'm going to check my outliers.

02:02 I'm going to see if i have any outliers going on in this upper end of this.

02:07 So to do that, we're going to take your iqr, which is going to be 7 .4.

02:13 Minus 6 .65, that's going to give us 0 .45 times 1 .5 means that we can only vary from that quartile by 0 .675.

02:29 Now, notice the distance from 7 .1 to 9 .0 is quite a bit more than that.

02:34 So what can that distance be? well, we're going to add it to that upper quartile, which gives me 7 .775.

02:45 I can't be any higher than that.

02:46 Anything over that is going to be outliers...

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