Question 17Which one of the following is NOT a valid statement about any frequency distribution?If the measure of skewness of a distribution is zero it must be symmetricIf the data are skewed to the left (negative skewness), the mean will be less than the medianFor a symmetric distribution the upper and lower quartiles will be equidistant from the medianThe mode of a symmetric distribution does not necessarily need to equal the median

The statement that is NOT valid about any frequency distribution is: "The mode of a symmetric distribution does not necessarily need to equal the median."

Here's why:

1. "If the measure of skewness of a distribution is zero it must be symmetric" - This is a valid statement. Skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable about its mean. If skewness is zero, the distribution is perfectly symmetric around the mean.

2. "If the data are skewed to the left (negative skewness), the mean will be less than the median" - This is also a valid statement. In a negatively skewed distribution, the mean is typically less than the median because the few low scores tend to pull the mean down.

3. "For a symmetric distribution the upper and lower quartiles will be equidistant from the median" - This is a valid statement. In a symmetric distribution, the median will be in the middle, and thus the upper and lower quartiles will be equidistant from it.

4. "The mode of a symmetric distribution does not necessarily need to equal the median" - This is NOT a valid statement. In a perfectly symmetric distribution, the mode, median, and mean are all equal. However, it's important to note that not all symmetric distributions are perfectly symmetric, and in those cases, the mode may not equal the median.