Question

You have just completed an experiment measuring the length (in mm) of 12 soybean plants after 3 days of sprouting. The measurements are listed below:

53 47 51 54 43 39 61 57 55 46 44 43

If you doubled every measurement in this dataset (e.g., 106, 94, 102, ...), what would the new IQR equal? (Think about the SD too!)

Answer 1

The new IQR is 22.

Explanation:

We are given the following data of length (in mm) of 12 soybean plants after 3 days of sprouting.

53, 47, 51, 54, 43, 39, 61, 57, 55, 46, 44, 43

Sorted data:

39, 43, 43, 44, 46, 47, 51, 53, 54, 55, 57, 61

Formula:

`IQR = Q_3 - Q_1\\Q_3 = \text{upper median},\\Q_1 = \text{ lower median}`

`Median:\\\text{If n is odd, then}\\\\Median = \displaystyle(n+1)/(2)th ~term \\\\\text{If n is even, then}\\\\Median = \displaystyle((n)/(2)th~term + ((n)/(2)+1)th~term)/(2)`

`Median ==(6^(th)+7^(th))/(2) (47+51)/(2) = 49`

`Q_1 =(3^(rd)+4^(th))/(2) = (43 + 44)/(2) = 43.5\\\\Q_3 =(9^(th)+10^(th))/(2)= (54 + 55)/(2) = 54.5`

IQR =
`Q_3 -Q_1 =54.5-43.5= 11`

If every measurement is doubled, then, the IQR will also double itself.

Thus,

New IQR =

`2* \text{IQR}\\=2\TIMES 11\\=22`

Thus, the new IQR is 22.