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For the data 2, 2, 3, 8, 10, which is larger — the mode or the median — and by how much?

Class 9StatisticsStatistics and Probability
  • AThe mode, by 1
  • BThey are equal
  • CThe median, by 1
  • DThe median, by 3

Step-by-Step Solution

The mode is 2, the only value that repeats. The data is already sorted and n = 5, so the median is the 3rd value = 3. The median is larger by 3 − 2 = 1.
Answer: C) The median, by 1

Key idea: Mode — the most frequent value

**Mode** = the observation that occurs the most times.

- **Unimodal**: 2, 3, 4, 4, 5, 6 → mode = 4.
- **Bimodal**: 1, 2, 2, 3, 3, 4 → modes 2 and 3.
- **No mode**: 1, 2, 3, 4 (each appears once — sometimes considered 'no mode').

For a frequency table, the mode is the value with the HIGHEST frequency.

Mode is useful for categorical data (most popular colour, most common shoe size). Mean and median don't apply there.

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