Question

What is the means-to-MAD ratio of the two data sets, expressed as a decimal?

Data set Mean Mean absolute deviation (MAD)
1 4.3 1
2 4.9 1.2

Answer 1

Means-to-MAD ratio is something that wouldn't be hard to find out, but I've certainly never even heard of it.

The mean (µ) of a set of data points is found by adding them up and dividing by the number of data points.

For our first set:
`\{1,\ 4.3,\ 1\}\rightarrow\frac{1+4.3+1}3=\frac{6.3}3=\boxed{2.1=\mu}`

For our second set:
`\{2,\ 4.9,\ 1.2\}\rightarrow\frac{2+4.9+1.2}3=\frac{8.1}3=\boxed{2.7=\mu}`

The mean absolute deviation is when you find the distance of each data point from the mean and then find the mean of those distances.

For our first set:
`\{1,\ 4.3\ 1\}\ has\ \mu=2.1.\\distances = \{1.1,\ 3.2,\ 1.1\}\rightarrow\frac{1.1+3.2+1.1}3=\frac{5.4}3=\boxed{1.8=MAD}`

For our second set:
`\{2,\ 4.9,\ 1.2\}\ has\ \mu=2.7\\distances=\{0.7,\ 2.2,\ 2.5\}\rightarrow\frac{0.7+2.2+2.5}3=\frac{5.4}3=\boxed{1.8=MAD}`

It wouldn't be hard to find the ratio between these for each set as the question asks...don't forget to put our ratio in simplest form!

For the first set:
`(\mu)/(MAD)=(2.1)/(1.8)=(21)/(18)=\boxed{\frac{7}6}`

For the second set:
`(\mu)/(MAD)=(2.7)/(1.8)=(27)/(18)=\frac{9}3=\boxed{\frac{3}1}`
(In a fraction, we would just put this as 3 because the ÷1 is redundant...however, because this is ratio, we have to keep it in)