Question

Range Rule of Thumb for Interpreting s The 20 brain volumes \((cm^{3})\) from Data Set 8 “IQ and Brain Size” in Appendix B have a mean of \(1126.0\ cm^{3}\) and a standard deviation of \(124.9\ cm^{3}\) . Use the range rule of thumb to identify the limits separating values that are significantly low or significantly high. For such data, would a brain volume of \(1440\ cm^{3}\) be significantly high?

Answer 1

Step 1
Range rule of thumb for identifying the significantly low or high values:
Significantly low values are identify by \(\mu-2\sigma\). The values lower than or equal to this \(\mu-2\sigma\) value are considered to be significantly low.
Significantly high values are identify by \(\mu+2\sigma\). The values higher than or equal to this \(\mu+2\sigma\) value are considered to be significantly high.
Step 2
Here, the significantly low and high values are calculated below:
\(\text{Signinficantly low }= 1.125-2(124.9)=875.2\)
\(\text{Signinficantly high }= 1.125+2(124.9)=1374.8\)
Step 3
Thus, the given value of brain volume with \(1,440 cm^{3}\) is significantly high because it is greater than \(1,374.8 cm^{3}\).