Which of the following statements are True? I. The mean of x, y, z is y. Then x + z = 2y. II. Median of 15, 28, 72, 56, 44, 32, 31, 43 and 51 is 43. III. Mode of 2, 3, 4, 5, 0, 1, 3, 3, 4, and 3 is…
Question and options
Which of the following statements are True?
- I. The mean of x, y, z is y. Then x + z = 2y.
- II. Median of 15, 28, 72, 56, 44, 32, 31, 43 and 51 is 43.
- III. Mode of 2, 3, 4, 5, 0, 1, 3, 3, 4, and 3 is 3.
Choose the correct answer from the given options:
- I and II only
- I and III only
- II and III only
- I, II and III
Answer and explanation
Correct answer: D - I, II and III
Statement I: (x+y+z)/3 = y gives x+z = 2y, so it is true. Statement II: sorted, the values are 15, 28, 31, 32, 43, 44, 51, 56, 72, and the middle (5th) value is 43, so it is true. Statement III: 3 occurs four times, more often than any other value, so the mode is 3 and it is true. All three statements hold.
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