Question

If a certain variable \(x\) divides a statistical data arranged in order into two equal parts; then the value of \(x\) is called the:

• A. mean
• B. median
• C. mode
• D. range

Answer 1

The Correct Option is B

Step 1: Understanding the problem:
In this problem, we are asked to identify the value of \( x \) that divides a statistical data set arranged in order into two equal parts. This value is commonly known as a measure of central tendency in statistics.

Step 2: Concept of dividing data into two equal parts:
To understand this concept, let’s first define what it means to divide a data set into two equal parts. When a data set is arranged in either ascending or descending order, the value of \( x \) that divides the data into two parts such that half of the data points are smaller than \( x \) and half are greater than \( x \) is called the **median**.

- The median is a central value in a data set. - If the number of data points is odd, the median is the exact middle value. - If the number of data points is even, the median is the average of the two middle values.

Step 3: Importance of the median:
The median is significant because it gives us the central value of the data set, separating it into two equal halves. This is particularly useful when the data is skewed or contains outliers. The median is less sensitive to extreme values than the mean (average), making it a more reliable measure of central tendency in such cases.

For example, consider the data set: \( \{1, 3, 4, 7, 9\} \). The number 4 is the median because it divides the data into two equal parts: \( \{1, 3\} \) and \( \{7, 9\} \). On the other hand, if the data set were \( \{1, 3, 4, 7, 9, 10\} \), the median would be calculated as the average of the two middle numbers (4 and 7), resulting in: \[ \text{Median} = \frac{4 + 7}{2} = 5.5 \]

Step 4: Conclusion:
Therefore, the value of \( x \) that divides a statistical data set into two equal parts is called the **median**. This is a fundamental concept in statistics that helps us understand the central tendency of a data set, especially when the data distribution is skewed or contains extreme values.