MEASURES OF CENTRAL TENDENCY
Definition Of Measures Of Central Tendency
A measure of central tendency is a measure that tells us where the middle of a bunch of data lies.
The three most common measures of central tendency are the mean, the median, and the mode.
More About Measures of Central Tendency
Mean: Mean is the most common measure of central tendency. It is simply the sum of the numbers divided by the number of numbers in a set of data. This is also known as average.
Median: Median is the number present in the middle when the numbers in a set of data are arranged in ascending or descending order. If the number of numbers in a data set is even, then the median is the mean of the two middle numbers.
Mode: Mode is the value that occurs most frequently in a set of data.
Examples of Measures of Central Tendency
For the data 1, 2, 3, 4, 5, 5, 6, 7, 8 the measures of central tendency are
Mean = 
Median = 5
Mode = 5
Video Examples: Measures of Central Tendency
Solved Example on Measures of Central Tendency
Ques: Find the measures of central tendency for the data set 3, 7, 9, 4, 5, 4, 6, 7, and 9.
Choices:
A. Mean = 6, median = 6 and modes are 4, 7 and 9
B. Mean = 6, median = 6 and mode is 4
C. Mean = 6, median = 6 and modes are 4 and 9
D. Mean = 6, median = 9 and modes are 4, 7 and 9
Correct Answer: A
Solution:
Step 1: Mean, median and mode of a data set are the measures of central tendency.
Step 2: Mean of the data set = 
[Formula.]
Step 3: 
[Substitute the values.]
Step 4: 
[Add the data values in the numerator and divide.]
Step 5: The data set in the ascending order is 3, 4, 4, 5, 6, 7, 7, 9, and 9. So, Median of the set is 6. [Median is the middle data value of the ordered set.]
Step 6: Mode is/are the data value(s) that appear most often in the data set. So, the modes of the data set are 4, 7 and 9.
Step 7: So, the measures of central tendency of the given set of data are mean = 6, median = 6 and modes are 4, 7, and 9.
Quick Summary
- Mean: The average of a dataset.
- Median: The middle value of an ordered dataset.
- Mode: The most frequently occurring value in a dataset.
🍎 Teacher Insights
Use real-world examples to illustrate the concepts. Engage students with interactive activities where they collect and analyze their own data.🎓 Prerequisites
- Basic arithmetic operations
- Understanding of data sets
Check Your Knowledge
Q1: What is the mean of the data set: 2, 4, 6, 8, 10?
Q2: What is the median of the data set: 1, 3, 5, 7, 9?
Q3: What is the mode of the data set: 2, 2, 3, 4, 5?
Frequently Asked Questions
Q: When should I use the median instead of the mean?
A: The median is more appropriate when the data set has outliers or is skewed, as it is less affected by extreme values.
Q: Can a data set have more than one mode?
A: Yes, a data set can be bimodal (two modes) or multimodal (more than two modes).