Question

If two groups of numbers have the same mean, then

a) Their standard deviations must also be equal
b) Their medians must also be equal
c) Their modes must also be equal
d) None of the above

Answer 1

Two groups of numbers with the same mean may have different standard deviations, medians, and modes because these statistics measure different aspects of the dataset. Thus, the correct answer is 'None of the above'.

Step-by-step explanation:

If two groups of numbers have the same mean, it does not automatically mean that they have the same standard deviations, medians, or modes. The mean is a measure of central tendency that gives the average value of a dataset, while:

• The standard deviation is a measure of dispersion that indicates how spread out the values are around the mean.
• The median is the middle value when the data are arranged in order.
• The mode is the most frequently occurring value in a dataset.

Two datasets can have the same mean but differ in how the values are distributed around that mean, leading to different standard deviations. Similarly, the arrangement of values can result in different medians and modes, regardless of the mean.

Therefore, the correct answer is:

d) None of the above