The weight of 6 students (in kg) are 14, 26,28, 20, 35, 30. find the median weight ?
The Correct Answer and Explanation is :
To find the median weight of the six students, follow these steps:
Step 1: Arrange the Weights in Ascending Order
The given weights are:
14, 26, 28, 20, 35, 30
Arranging them in increasing order:
14, 20, 26, 28, 30, 35
Step 2: Find the Median
The median is the middle value of an ordered dataset. Since there are 6 numbers (even count), the median is found by averaging the 3rd and 4th values:
[
\text{Median} = \frac{\text{3rd value} + \text{4th value}}{2}
]
[
= \frac{26 + 28}{2}
]
[
= \frac{54}{2} = 27
]
So, the median weight is 27 kg.
Explanation:
The median represents the middle value of a dataset when arranged in ascending order. It is a measure of central tendency, meaning it shows the typical value in a dataset. Unlike the mean (average), the median is not affected by extreme values (outliers), making it a more reliable representation of the dataset’s center.
In this case, we had an even number of observations (6 weights), so we took the average of the two middle values. If the dataset had an odd number of values, the median would be the exact middle number.
The importance of median is seen in various fields, such as:
- Education: To analyze student performances.
- Economics: To understand income distribution.
- Medicine: To evaluate health statistics.
By using the median instead of the mean, we get a more balanced view of the dataset, unaffected by extreme values.
Now, I will generate an image to visualize this concept.
Here is a visual representation of the student weights, with the median weight (27 kg) marked by a red dashed line. This helps illustrate how the median divides the dataset into two equal halves. Let me know if you need any modifications!