Question

Name an example of a real-world data set, not yet mentioned in the course, where you would typically expect to see a normal distribution. Be sure to describe what the labels would be for the horizontal and vertical axis of the display. Then explain why you would expect a normal distribution. What range of data values would you expect to represent 1 standard deviation from the mean?

Answer 1

The data sets of errors of a measurement, height, weight, length and temperature generally follow normal or approximately normal distribution.

For these data sets, most of the values cluster in the center and the remaining are spread off symmetrically on either extremes. So, the data are denser in the center and less dense in the tails and forms a symmetrical distribution. So, we would expect a normal distribution for these data sets.

On X-axis: the units of variable (say, height in centimetres).

On Y-axis: probability density function (pdf).

By the emperical rule of a normal distribution, 68% of data values would be expected to represent 1 standard deviation from the mean on either side (34% to the left of the mean and 34% to the right of the mean).