In a normal curve, the mean, median, and mode are not equal to each other.
True
False
The correct answer and explanation is:
The correct answer is False.
In a normal distribution, the mean, median, and mode are all equal to each other. This is a key characteristic of a perfectly symmetric, bell-shaped curve. In a normal distribution, the data is symmetrically distributed around the central peak, which means that the mean (average), median (middle value), and mode (most frequent value) all fall at the same point.
The mean is the sum of all data values divided by the number of values, representing the “center” of the data. The median is the middle value when the data is ordered from lowest to highest. In a perfectly symmetrical distribution, this middle value will also align with the mean. The mode represents the value that appears most frequently in the data set, and in a symmetric curve, the highest point of the curve (where the data peaks) coincides with both the mean and the median.
This equality of the mean, median, and mode is one of the defining features of a normal distribution. The symmetry of the normal curve ensures that all three measures of central tendency are located at the same point. However, this only holds for a normal distribution. If the data is skewed (i.e., not symmetrical), the mean, median, and mode will not coincide. For instance, in a positively skewed distribution, the mean will be greater than the median, and the median will be greater than the mode.
In summary, for a normal distribution, the mean, median, and mode are always equal, making the statement in the question false.