Multiple choice

Which of the following does not change for the observation $23, 50, 27, 2x, 48, 59, 72, 89, 5x, 100, 120$ when $x$ lies between $15$ and $20$?

  1. Arithmetic mean

  2. Range

  3. Median

  4. Quartile deviation
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B Correct answer
AI explanation

As the variable x varies between 15 and 20, the values of the terms 2x and 5x also change, which alters the sum of the data and therefore shifts the arithmetic mean. The lowest observation is 23 and the highest observation is 120, and since neither depends on x, the difference between the maximum and minimum values remains constant at 97; therefore, the range does not change.

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