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
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