Which of the following is correct about mode?a)It is central.b)It occu...
B) It occurs most frequently.
The mode is a measure of central tendency that represents the value or values that occur most frequently in a dataset. In other words, it is the value that appears with the highest frequency.
Explanation:
- The mode is the only measure of central tendency that focuses on the frequency of values rather than their magnitude. It is particularly useful when dealing with categorical or discrete data.
Example:
Let's consider the following dataset of exam scores: 75, 85, 90, 75, 80, 85, 75, 90, 85, 80.
To determine the mode, we need to identify the value(s) that occur most frequently. In this case, the value "75" appears three times, while all other values appear twice. Therefore, the mode of this dataset is 75.
- It is important to note that a dataset can have more than one mode if there are multiple values that occur with the same highest frequency. For example, if the dataset was: 75, 85, 90, 75, 80, 85, 75, 90, 80, 80, then both 75 and 80 would be modes since they both occur three times, while all other values occur twice.
- Unlike the mean and median, the mode can be applied to both numerical and categorical data. For example, in a dataset of favorite colors (e.g., red, blue, green, red, yellow, blue, blue), the mode would be "blue" since it occurs most frequently.
- The mode is not influenced by extreme values or outliers, making it a robust measure of central tendency. This means that even if there are values that occur significantly more or less frequently than others, they do not affect the mode.
- It is important to note that the mode is not always applicable or meaningful for every dataset. For example, in a dataset with no repeated values (e.g., 10, 20, 30, 40), there is no mode since no value occurs more frequently than others.
In conclusion, the mode is the measure of central tendency that represents the value or values that occur most frequently in a dataset, making option b) "It occurs most frequently" the correct statement about the mode.