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

Answer:

The new IQR is 22.    

Step-by-step 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:

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

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

$Median ==\dfrac{6^{th}+7^{th}}{2} \dfrac{47+51}{2} = 49$

$Q_1 =\dfrac{3^{rd}+4^{th}}{2} = \dfrac{43 + 44}{2} = 43.5\\\\Q_3 =\dfrac{9^{th}+10^{th}}{2}= \frac{54 + 55}{2} = 54.5$

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 =

$2\times \text{IQR}\\=2\TIMES 11\\=22$

Thus, the new IQR is 22.