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}](https://tex.z-dn.net/?f=IQR%20%3D%20Q_3%20-%20Q_1%5C%5CQ_3%20%3D%20%5Ctext%7Bupper%20median%7D%2C%5C%5CQ_1%20%3D%20%5Ctext%7B%20lower%20median%7D)
![Median ==\dfrac{6^{th}+7^{th}}{2} \dfrac{47+51}{2} = 49](https://tex.z-dn.net/?f=Median%20%3D%3D%5Cdfrac%7B6%5E%7Bth%7D%2B7%5E%7Bth%7D%7D%7B2%7D%20%5Cdfrac%7B47%2B51%7D%7B2%7D%20%3D%2049)
![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](https://tex.z-dn.net/?f=Q_1%20%3D%5Cdfrac%7B3%5E%7Brd%7D%2B4%5E%7Bth%7D%7D%7B2%7D%20%3D%20%5Cdfrac%7B43%20%2B%2044%7D%7B2%7D%20%3D%2043.5%5C%5C%5C%5CQ_3%20%3D%5Cdfrac%7B9%5E%7Bth%7D%2B10%5E%7Bth%7D%7D%7B2%7D%3D%20%5Cfrac%7B54%20%2B%2055%7D%7B2%7D%20%3D%2054.5)
IQR = ![Q_3 -Q_1 =54.5-43.5= 11](https://tex.z-dn.net/?f=Q_3%20-Q_1%20%3D54.5-43.5%3D%2011)
If every measurement is doubled, then, the IQR will also double itself.
Thus,
New IQR =
![2\times \text{IQR}\\=2\TIMES 11\\=22](https://tex.z-dn.net/?f=2%5Ctimes%20%5Ctext%7BIQR%7D%5C%5C%3D2%5CTIMES%2011%5C%5C%3D22)
Thus, the new IQR is 22.