Make up three data sets with 5 numbers each that have a the...

Make up three data sets with 5 numbers each that have: a. the same mean but different standard deviations. b. the same mean but different medians. c. the same median but different means.

Transcript

00:01 We want to make up some data sets with five numbers that meet some different criteria.

00:06 And if we look at b and c, those are directly contradictory.

00:11 You can't have data sets that have the same mean but different medians, and also the same median but different means.

00:18 So i will answer each of these one by one, starting with a.

00:22 We want the same mean but different standard deviations.

00:26 To make our lives easier, i'm going to set the mean as being zero, and i'm also going to have a value of zero in the data sets.

00:34 The mean is a measure of center.

00:37 To calculate the mean, you take each value in the data set, add them all up, divide by the number of pieces of data.

00:45 So it's just an average.

00:47 Standard deviation is a measure of spread.

00:53 It tells you how much variety there is to the data.

00:56 Take each value, subtract the mean, mu, square the difference, add them all up, divide by the number of pieces of data, square root them.

01:05 A bit more effort, but the basic thing is it's based on the differences between each value and the mean.

01:12 So for my first data set, i'm going to have a standard deviation of zero.

01:18 All of the data is the same.

01:19 There is no spread.

01:21 You can never have a negative standard deviation.

01:24 You can't have negative spread.

01:26 You can have a standard deviation of zero if every piece of data in the set is the same.

01:33 Then i'm going to have something with very low standard deviation.

01:38 So you can see the center here is...

01:39 Oops, actually that should be minus one.

01:42 There we go.

01:44 So you can see the center here is zero, so the mean is zero, but the spread is not zero.

01:52 It's a little bit higher than that.

01:53 And then we can have another data set with slightly higher standard deviation.

02:07 That's a.

02:08 Part b.

02:09 Same mean, different medians.

02:11 So a median is a measure of center.

02:18 So if you have a data set and you order it from smallest to largest, the median is right in the middle.

02:26 So if there are five numbers, it will be the third number in the data set...

Question

Make up three data sets with 5 numbers each that have: a. the same mean but different standard deviations. b. the same mean but different medians. c. the same median but different means.

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