Examples on Relation between Mean, Median and Mode
Example 1: The median and mode for a given set of data points is 20 and 30 respectively. Find out the mean. (Assume a moderately skewed distribution)
Solution:
Given,
Mode = 30, Median = 20
To find the Mean:
Mode = 3×Median − 2×Mean
30=3×20−2×Mean
30=60−2×Mean
2×Mean=30
Mean=15
Example 2: The mean and mode for a given set of data points is 20 and 30 respectively. Find out the mean. (Assume a moderately skewed distribution)
Solution:
Given:
Mode = 25, Mean = 12
To find the Median:
Mode=3×Median−2×Mean
25=3×Median−2×12
25=3×Median−24
3×Median=49
Median≈16.33
Example 3: The median and mean for a given set of data points is 15 and 10 respectively. Find out the mean. (Assume a moderately skewed distribution)
Solution:
Given:
Median = 15, Mean = 10
To find the Mode:
Mode=3×Median−2×Mean
Mode=3×15−2×10
Mode=45−20
Mode=25
Example 4: For a symmetrical distribution, the value of mean is 42. What can we say about the value of median and mode?
Solution:
For a symmetrical distribution, the value of mean, median and mode are approximately equal.
Hence,
Median = Mode = Mean = 42
Example 5: For a positively skewed distribution, the value of mean is 42 and mode is 20. What can we say about the value of median?
Solution:
For a positively skewed frequency distribution, the value of mean, median and mode has the following relation:
Mean > Median > Mode
For Mean = 42, and Mode = 20, we can say that the value of median lies in the range of 20 to 42.
Relation between Mean, Median and Mode
Relation between the Mean, Median, and Mode is the difference between the thrice of the median and twice of the mean gives Mode. Mode Mean, median, and mode are fundamental statistics measurements that give valuable insights into a given dataset. They represent the central tendency of the dataset. Although their values differ from each other for a given dataset they are closely related to each other.
In this article, we’ll learn the concepts of relation between mean, median, and mode and explore the connections between them.
Table of Content
- Mean Definition
- Median Definition
- Mode Definition
- Relation between Mean, Median and Mode
- Relation between Mean, Median and Mode with Frequency Distribution
- Examples on Relation between Mean, Median and Mode
- Practice Questions on Relation between Mean, Median and Mode