Single correct option
Consider the following statements:
1. Adding the same constant to every observation does not change the variance.
2. The median of a data set is always equal to its mean.
Which of the statements given above is/are correct?
1. Adding the same constant to every observation does not change the variance.
2. The median of a data set is always equal to its mean.
Which of the statements given above is/are correct?
- A. 1 only
- B. 2 only
- C. Both 1 and 2
- D. Neither 1 nor 2
Show answer and solution
Answer: (A) 1 only
Adding a constant shifts every observation and the mean by that constant, so the deviations from the mean are unchanged and the variance stays the same; statement 1 is true. The median and mean are equal only for symmetric data, such as 1, 2, 3; for 1, 2, 9 the median is 2 but the mean is 4. Statement 2 is false.
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