If the mode of the data set a, a + 2, a + 4, a + 6, a + 6, a + 6, a + 8 is 26, find a.

Question

If the mode of the data set a, a + 2, a + 4, a + 6, a + 6, a + 6, a + 8 is 26, find a.

1. A. 30
2. B. 20 (Correct answer)
3. C. 40
4. D. 10

Correct Answer

Option B — 20

Detailed Solution & Explanation

The correct answer is 20.

Key Points

• The mode is the value occurring most often. In the set {a, a+2, a+4, a+6, a+6, a+6, a+8}, the term a + 6 appears three times while every other appears once.
• So a + 6 = 26, giving a = 20.

Additional Information

• Check by substituting: the set becomes {20, 22, 24, 26, 26, 26, 28}, whose mode is clearly 26 ✓.
• The three measures of central tendency: mean (arithmetic average), median (middle value once ordered) and mode (most frequent). This set's median is also 26, since it is the fourth of seven ordered values.
• A data set may be unimodal, bimodal or have no mode at all if every value occurs equally often.
• For grouped data the mode is estimated by l + h(f₁ − f₀)/(2f₁ − f₀ − f₂), where f₁ is the modal class frequency.
• The empirical relationship Mode ≈ 3 × Median − 2 × Mean is worth knowing for questions supplying two of the three.