what does 42 represent in the data set. 48,40,52,42,40
The Correct Answer and Explanation is:
In the dataset 48, 40, 52, 42, 40, the number 42 represents a data point, just like the other numbers. Specifically, it is one of the values in the set, and it contributes to the overall statistical characteristics of the data, such as the mean, median, mode, range, and distribution.
Detailed Explanation
To understand what 42 represents in this dataset—48, 40, 52, 42, 40—we can analyze its position and significance using basic statistical tools.
First, arrange the numbers in ascending order:
40, 40, 42, 48, 52
Now, let’s explore the role of 42 in several statistical measures:
- Median:
The median is the middle number when data is ordered. Here, the third number is 42, making it the median of the dataset. So, 42 represents the central value. - Mean (Average):
Add all values: 48 + 40 + 52 + 42 + 40 = 222
Divide by the number of values (5): 222 ÷ 5 = 44.4
While 42 is close to the mean, it is slightly below it. This shows it’s near average, helping to pull the mean slightly downward. - Mode:
The number 40 appears twice, more than any other number, so 40 is the mode. 42 appears only once and is not the most frequent value. - Range:
Maximum – Minimum = 52 – 40 = 12
42 falls within this range and shows a mid-range value.
Conclusion:
In this dataset, 42 serves as the median, making it statistically significant. It is not the highest or lowest value but represents the center point of the data. This makes 42 important when analyzing the dataset’s balance or distribution. It is also close to the mean, indicating that it helps stabilize the average. Though it is not the mode, it remains crucial for understanding the dataset’s shape and spread.
