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Answer
The median of the data is approximately 27.55.
Solution
We start with the median formula for grouped data
where
-
is the lower class boundary of the median class, -
is the class width, -
is the total frequency, -
is the cumulative frequency up to (but not including) the median class, and -
is the frequency of the median class.
Given the frequency table
- First, calculate
. The total frequency is
-
Locate the median class. The cumulative frequencies show:
- Up to the 10–20 class:
- Up to the 21–30 class:
Sinceis greater than and less than or equal to , the median falls in the class. - Up to the 10–20 class:
-
Identify the parameters for the median class:
- Lower class boundary,
(assuming the conventional correction for grouped data) - Class width,
- Frequency of the median class,
- Cumulative frequency before the median class,
- Lower class boundary,
-
Substitute these values into the formula:
- Compute the value inside the fraction:
- Multiply by the class width:
- Finally, add the lower boundary:
Thus, the median of the data is approximately
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Simplify this solution Extra Insights
Let’s dive into the history behind class intervals and histograms! The concept dates back to the early days of statistics in the 19th century. Pioneers like Karl Pearson and Francis Galton worked extensively on distributing data into manageable chunks using class intervals, making it easier to visualize and understand information trends. This technique laid the groundwork for modern data analysis and the creation of graphical representations like histograms!
Now, onto a real-world application! Class intervals are not just for textbooks; they are used by businesses to analyze sales data. For instance, a retail store might group sales by price ranges to discover which intervals generate the most revenue. This helps to fine-tune marketing strategies, focus inventory, and tailor customer experiences, ensuring that products are priced just right for their target audience!
