Question

Consider two normal distributions, one with mean -4 & standard deviation 3 or the one with mean -4 and standard deviation 6. Answer true or false to each statement and explain your answers

a. The two normal distributions have same spread

b. The two normal distributions are centred at the same place.

Short answer

A. The two normal distributions have same spread : False

B. The two normal distributions are centred at the same place : True

Step-by-step solution

Spread Concept and False

Spread is a measure of variability of data around the mean, it indicates on average that how scattered the other values are around mean.

Standard Deviation is a statistical measure of dispersion. It is the under root of average squared deviations around mean.

So as the standard deviation of both distributions are unequal, ie 3 and 6 respectively. So, they don't have same spread

Centre Concept & True

Centre of the distribution denotes the measures of central tendency, which is most prominently arithmetic mean.

As the means of distributions are equal ie -4, so there centre is equal.