The pair of averages whose value can be determined graphically.
Options
AMean and Median
BMode and Mean
CMode and Median
DNone of these
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Statistical Description of DataMTP June 24 Series IIIQuestion 2677 of 295
All Questions Correct Answer
✅ Option c — Mode and Median
All Options:
- AMean and Median
- BMode and Mean
- CMode and Median
- DNone of these
Detailed Solution & Explanation
We analyze the graphical determination of different measures of central tendency:
1. **Median**: The median can be graphically determined by plotting cumulative frequency curves, also known as **Ogives**. By constructing the 'less-than' and 'more-than' ogives, their point of intersection projected onto the horizontal axis (-axis) yields the value of the median. Alternatively, one can find the value of corresponding to the cumulative frequency of on a single ogive.
2. **Mode**: The mode can be graphically determined using a **Histogram**. In a histogram of a continuous frequency distribution, the modal class is represented by the tallest rectangle. By drawing two diagonal lines from the upper corners of the tallest rectangle to the adjacent upper corners of the neighboring rectangles, the -coordinate of the intersection point of these diagonals gives the mode.
3. **Mean**: The arithmetic mean cannot be determined graphically as its calculation requires summing all individual observations, which is not represented directly in cumulative or grouped graphical structures like ogives or histograms.
Thus, the pair of averages that can be determined graphically is the Mode and Median, which corresponds to Option C.
Hence, **Option C** is the correct answer.
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