Which of the following is used to determine the mode of a grouped data?

Analyze the question: We're asked which graph is used to find the mode of grouped data.

Explain the concept: The mode is the value that occurs most often. For grouped data, we look for the modal class (the class with the highest frequency) and then estimate the mode from the graph.

• Bar chart: used for discrete or categorical data, and it is not used to estimate the mode of grouped continuous data.
• Frequency polygon: it shows the shape of the distribution, but it is not the standard tool for finding the mode.
• Ogive (cumulative frequency curve): used to find the median, quartiles, and percentiles. It cannot give the mode.
• Histogram: the standard graph for grouped data. The tallest bar shows the modal class. To estimate the mode, draw lines from the top corners of the tallest bar to the top corners of the neighbouring bars. The point where the lines cross, dropped down to the horizontal axis, gives the mode.

Solution steps:

1. Draw the histogram of the grouped data.
2. Identify the tallest bar, which is the modal class.
3. Join the top-left corner of the modal bar to the top-left corner of the bar after it, and join the top-right corner of the modal bar to the top-right corner of the bar before it.
4. From the point where the two lines cross, drop a vertical line to the x-axis. The reading is the mode.

Answer: The histogram, which is option D.

Exam tip: Remember the pairings:

• Histogram → Mode
• Ogive → Median and quartiles