7) What is the relationship of the Mean, Median and Mode as Measures of Central Tendency in a true Normal Curve?
A. They are equal
B. They align Median, Mode and Mean in that order
C. They align Mean, Median and Mode in that order
D. They align Mode, Median and Mean in that order
a. they are equal
The relationship of the Mean, Median, and Mode as measures of central tendency in a true Normal Curve is that they all align in that order: Mean, Median, and Mode.
To understand why this is the case, let's break down each measure of central tendency and its relationship to a normal distribution:
1. Mean: The mean is the average value of a dataset. In a normal distribution, the mean is located exactly at the center of the curve. It is the balancing point of the distribution, with symmetrical data on both sides. Because of the symmetry, the mean coincides with both the median and mode.
2. Median: The median is the middle value of a dataset when it is arranged in ascending or descending order. In a normal distribution, the median is also located at the center of the curve. As mentioned earlier, since the normal distribution is symmetrical, the middle value is also the mean. Thus, the median aligns with the mean.
3. Mode: The mode is the value that occurs most frequently in a dataset. In a normal distribution, there can be multiple modes if there are repeated values with the same frequency. However, in a perfectly normal distribution, where all values have different frequencies, there is no mode. This is because no single value occurs more frequently than others. Therefore, the mode does not align with the mean and median in a true normal curve.
Given this explanation, the correct answer is:
C. They align Mean, Median, and Mode in that order.