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} an

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?

2021-02-14

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 $$1,374.8 cm^{3}$$.