Question

Range Rule of Thumb for Interpreting s The 20 brain volumes (cm3 ) from Data Set 8 “IQ and Brain Size” in Appendix B have a mean of 1126.0 cm3 and a standard deviation of 124.9 cm3. 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 cm3 be significantly high?

Short answer

According to the range rule of thumb, values that lie above 1375.8${\text{cm}}^3$ are significantly high, and values that lie below 876.2 ${\text{cm}}^3$are significantly low.

The value of the brain volume equal to 1440 will be significantly high.

Step-by-step solution

Given information

The total brain volume (in ${\text{cm}}^3$) of 20 twins is proved in the dataset.

The mean volume is equal to 1126.0 ${\text{cm}}^3$.

The standard deviation is equal to 124.9 ${\text{cm}}^3$.

Identifying the limits 

The significant values of mathematical data can be identified using the range rule of thumb, which states that values

• equal to or less than$\mu -\sigma$ are considered to be significantly low values.
• equal to or greater than$\mu +\sigma$ are considered to be significantly high values.
• between $\mu -\sigma$and $\mu +\sigma$ are not considered to be significant values.

Here, $\mu$stands for the mean of the data, and $\sigma$stands for the standard deviation of the data.

So, the limits become as shown below:

Lower limit:

$$\begin{gathered} \mu -2\sigma =1126.0-2\times 124.9 \\ =1126.0-249.8 \\ =876.2 \end{gathered}$$.

Upper limit:

.$$\begin{gathered} \mu +2\sigma =1126+2\times 124.9 \\ =1126+249.8 \\ =1375.8 \end{gathered}$$

For the given brain volumes, the limit-separating values are , which implies that the values below 876.2 ${\text{cm}}^3$are significantly low, and those above 1375.8 ${\text{cm}}^3$are significantly high.

Checking for significance

If the value lies between the limits, it is not significant, and if it lies beyond the limits, it is significant.

The total brain volume equal to 1440${\text{cm}}^3$ lies beyond the upper limit of 1375.8${\text{cm}}^3$ . Therefore, it is significantly high.