Question

In which two measures of central tendency do not affect the outliers?
A) median and mean
B) mean and mode
C) median and mode
D) mode and range

Answer 1

Hint: The measure of central tendency is a statistic that represents the typical central value of the data set. This value indicates where most values in a distribution fall are also referred to as the central location of a distribution. The three most common measures of central tendency in statistics are mean, median, and mode. They are used to indicate the central point using a different method.

Complete step by step answer:
 Mean is the most popular and well known used to measure central tendency. It can be used with both discrete and continuous data even though it is most often used with continuous data. The mean is the ratio of the sum of all the values of given data to the total numbers of values in the given data set.
 \[x = \dfrac{{\sum x }}{n}\]
- Median is the middle score of a data set that has been arranged in order of the magnitude. The median is less affected by the outliner and the skewed data. To find the median arrange the data from smallest to largest and find the data point that has an equal amount of that value above and below it.
- The mode is the most frequent score in the data set less affected by the outliner. On the histogram, it is represented by the highest bar in a bar chart or the histogram.
- The range is a measure by which the values in the data set are likely to differ from their mean. The range is easily calculated by subtracting the lowest from the highest value.
- Hence we can say median and mode are the two measures of central tendency, which does not affect the outliers.

Hence the correct answer is Option ‘C’.

Note: Students must not get confused; outliner is just a data point that differs significantly from other observations. Outliner mainly occurs due to variability in the measurement or due to experimental errors.