**Median is a statistical measure that represents the middle value of a dataset. **

**To find the median, you first need to arrange the data in order from smallest to largest or largest to smallest, depending on the dataset. **

**Once you have the data in order, you find the value that is exactly in the middle of the dataset.**

**If the dataset has an odd number of values, the median is the middle value. **

**If the dataset has an even number of values, the median is the average of the two middle values.**

**Example 1:**

**let’s say we have the following dataset:**

**{1, 3, 5, 7, 9}**

**To find the median, **

**we first need to arrange the data in ascending or descending order:**

**{1, 3, 5, 7, 9}**

**Since the dataset has an odd number of values, **

**we can easily find the middle value, which is 5. **

**Therefore,the median of this dataset is 5.**

**Example 2:**

**Now let’s consider a dataset with an even number of values:**

**{2, 4, 6, 8}**

**To find the median, **

**Again, we arrange the data in ascending or descending order:**

**{2, 4, 6, 8}**

**This time, we have an even number of values,**

**so we need to find the average of the two middle values. T**

**the middle values are 4 and 6, **

**so the average is (4 + 6) / 2 = 5. **

**So,the median of this dataset is 5.**

**Question 1:**

**let’s say we have the following dataset arranged in ascending order:**

**{1, 3, 5, 7, 9, 11}**

**This dataset has an odd number of values, **

**So,the median is the middle value, which is 5.**

**Requested by: Ameer**

**Question 2:**

**Now let’s consider a dataset with an even number of values arranged in ascending order:**

**{2, 4, 6, 8, 10, 12}**

**The two middle values are 6 and 8, **

**so the average of these values is (6 + 8) / 2 = 7. **

**Therefore, the median of this dataset is 7.**

**Requested by: Ameer**

**Question 1:**

**let’s say we have the following dataset arranged in descending order:**

**{11, 9, 7, 5, 3, 1}**

**This dataset has an odd number of values, **

**so the median is the middle value, which is 7.**

**Requested by: Ameer**

**Question 2:**

**Now let’s consider a dataset with an even number of values arranged in descending order:**

**{12, 10, 8, 6, 4, 2}**

**The two middle values are 8 and 6, but this time in reverse order. **

**Therefore, the average of these values is (8 + 6) / 2 = 7. **

**Therefore, the median of this dataset is 7.**

**Requested by: Ameer**

**Practice Problems**

**Q1.Find the median of the following set of numbers: 2, 3, 5, 7, 9, 10, 12, 13, 15**

**Answer: 9**

**Q2.Find the median of the following set of numbers: 1, 3, 5, 7, 9, 11, 13**

**Answer: 7**

**Q3.Find the median of the following set of numbers: 2, 5, 8, 10, 12, 16**

**Answer: 9**

**Q4.Find the median of the following set of numbers: 4, 6, 8, 10, 12**

**Answer: 8**

**Q5.Find the median of the following set of numbers: 3, 3, 5, 7, 8, 10, 12**

**Answer: 7**

**Q6.Find the median of the following set of numbers: 1, 2, 3, 4, 5, 6, 7, 8, 9**

**Answer: 5**

**Q7.Find the median of the following set of numbers: 2, 4, 6, 8, 10, 12, 14, 16**

**Answer: 9**

**Q8.Find the median of the following set of numbers: 2, 3, 3, 4, 5, 6, 8, 10**

**Answer: 4.5**

**Q9.Find the median of the following set of numbers: 4, 7, 10, 13, 15, 19, 22, 25**

**Answer: 14**

**Q10.Find the median of the following set of numbers: 1, 3, 4, 6, 7, 9, 11, 13, 15**

**Answer: 7**

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**Mode:**

**In statistics, mode refers to the value that appears most frequently in a set of data. **

**It is a measure of central tendency that is useful when trying to describe the most typical or common value in a set.**

**To find the mode, you simply need to identify which value appears most often in the data set. **

**If there is more than one value that appears with the same frequency and more frequently than any other value, the data set is said to have multiple modes.**

**Question 1:**

**Find the mode of the following data set: 2, 4, 6, 8, 8, 10, 12.**

**Solution:**

**The value 8 appears twice in this data set, which is more often than any other value. **

**So,the mode of this data set is 8.**

**Requested by: Ahsan**

**Question 2:**

**Find the mode of 1, 2, 2, 3, 3, 3, 4, 4, 4, 4.**

**Solution:**

**The value 4 appears four times in this data set, which is more often than any other value. **

**So,the mode of this data set is 4.**

**Requested by: Ahsan**

**Question 3:**

**Find the mode of 1, 2, 3, 4, 5.**

**Solution:**

**There is no value that appears more than once in this data set **

**so there is no mode.**

**Requested by: Ahsan**

**Question 4:**

**Find the mode of 2, 4, 6, 8, 10, 12.**

**Solution:**

**There is no value that appears more than once in this data set**

**so there is no mode.**

**Requested by: Ahsan**

**Question 5:**

**Find the mode of the following data set: 1, 1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 5, 5, 5.**

**Solution:**

**The value 5 appears five times in this data set **

**Therefore,the mode of this data set is 5.**

**Requested by: Ahsan**

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