Question

Suppose that a biologist states that the average height of undergraduate students at your university is 205 cm plus or minus a standard deviation of 17cm. What does this mean?

Answer 1

The average height stated by the biologist means that most undergraduate students' heights cluster around 205 cm, deviating by 17 cm on average. This deviation is a measure of the spread of height values around the mean in a normal distribution.

Step-by-step explanation:

When a biologist states that the average height of undergraduate students at your university is 205 cm with a standard deviation of 17 cm, it implies that heights are normally distributed around a mean (or average) value of 205 cm. The standard deviation indicates that the majority of the students' heights will fall within 17 cm above or below the mean value. In a normal distribution, about 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.

For instance, using similar values given in the provided references, if we were to consider the height of 15-to 18-year-old males from Chile in 2009-2010 with a mean height of 170 cm and a standard deviation of 6.28 cm, and we have an individual whose height is 168 cm, we can calculate a z-score to understand how this individual's height compares to the overall population.

Answer 2

This means that the means height (which is all the sum of the height of all the students divided by their number ) is 205 cm. Standard deviation means how the height of the students deviates from this mean since students do vary in height and are not all the same height of 205 cm. Therefore, in this case, the amount of standard dispersion of the students' height is by 17 cm on either lower or higher side of the mean.