Answer and Explanation: The answer is D. The statement "For an even number of observations, the median is the mean of the two middle numbers" is correct as in case...
Key Takeaways. The median is the middle number in a sorted, ascending or descending, list of numbers and can be more descriptive of that data set than the average. The median is sometimes used as opposed to the mean when there are outliers in the sequence that might skew the average of the values.
You find the mean (informally called the average) by adding up all the numbers in a set and then dividing by how many values there are. When you arrange a set of values from smallest to largest, the median is the one in the middle. The mode is simply the value that occurs the most in the set.
Outliers affect the mean value of the data but have little effect on the median or mode of a given set of data.
Median PropertiesMedian is not dependent on all the data values in a dataset.The median value is fixed by its position and is not reflected by the individual value.The distance between the median and the rest of the values is less than the distance from any other point.Every array has a single median.More items...
The median is the most informative measure of central tendency for skewed distributions or distributions with outliers. For example, the median is often used as a measure of central tendency for income distributions, which are generally highly skewed.
Median is not dependent on all observations of a data especially not dependent on extreme values. It can be determined graphically. From the above properties of a median, it is clear that option number 3 i.e "It is based on all observations of a data" is not correct.
Which Is More Accurate? The mean is the most accurate way of deriving the central tendencies of a group of values, not only because it gives a more precise value as an answer, but also because it takes into account every value in the list.
Median and Sample Size Similarly, the median scores will be unduly influenced by a small sample size. If only five students took a test, a median score of 83 percent would mean that two students scored higher than 83 percent and two students scored lower.
In fact, adding a data point to the set, or taking one away, can effect the mean, median, and mode. If we add a data point that's above the mean, or take away a data point that's below the mean, then the mean will increase.
The median is less affected by outliers and skewed data than the mean, and is usually the preferred measure of central tendency when the distribution is not symmetrical. Limitation of the median: The median cannot be identified for categorical nominal data, as it cannot be logically ordered.
The outlier does not affect the median. This makes sense because the median depends primarily on the order of the data. Changing the lowest score does not affect the order of the scores, so the median is not affected by the value of this point. The mean is not a good summary of this student's homework scores.