Question

The brain volumes ​(cm cubed​) of 20 brains have a mean of 1068.2 cm cubed and a standard deviation of 123.3 cm cubed. Use the given standard deviation and 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 1354.8 cm cubed be significantly​ high?

Answer 1

Yes, a brain volume of 1354.8
`cm^3` is significantly​ high.

Explanation:

From the information given we know:

• Standard deviation is 123.3
  `cm^3`

• Mean: 1068.2
  `cm^3`

The range rule of thumb can be used to estimate the largest and smallest data values of a data set.

Largest data value = mean + 2 * standard deviation

Smallest data value = mean - 2 * standard deviation

So

Largest data value =
`1068.2 + 2\cdot 123.3 = 1314.8 \:cm^3`

Smallest data value =
`1068.2 - 2\cdot 123.3 = 821.6 \:cm^3`

Note that a brain volume of 1354.8
`cm^3` is not in the range of the smallest and largest value. Therefore this value is significantly​ high.