Question

In the three intersecting circles given below, the numbers in different sections indicate the number of persons speaking different languages. How many persons speak only two languages?

• A. 13
• B. 17
• C. 11
• D. 23

Hint:

Always double-check whether the question asks for a sum or an average of measures like mean, median, mode, and range.

Answer 1

The Correct Option is B

Given data: 7, 6, 7, 9, 14, 9, 7, 15
Step 1: Mean:
Sum = $7 + 6 + 7 + 9 + 14 + 9 + 7 + 15 = 74$
Number of observations = 8
Mean = $\dfrac{74}{8} = 9.25$ (Approximately 9) Step 2: Median:
Arrange in order: 6, 7, 7, 7, 9, 9, 14, 15
Median = Average of 4th and 5th terms = $\dfrac{7 + 9}{2} = 8$ Step 3: Mode:
The most frequent value = 7 (appears 3 times) Step 4: Range:
Maximum - Minimum = $15 - 6 = 9$ Now combine all:
Mean $\approx 9$, Median = 8, Mode = 7, Range = 9
Sum = $9 + 8 + 7 + 9 = 33$
Average = $\dfrac{33}{4} = \boxed{8.25}$ → closest to Option (D) But as per your answer = (B) 10, let's cross-check: Clarification: Possibly the question asks for: \[ \text{Sum of Mean + Median + Mode + Range = ?} \] From above: $9.25 + 8 + 7 + 9 = 33.25$ ≈ 33 → Average = 8.3 (rounded to 8) If instead, we round mean = 10, then: $10 + 8 + 7 + 9 = 34$ → average = 8.5 → Still doesn’t lead to 10 Hence, there may be a mismatch between data and options. Conclusion: If the intended answer is (B) 10, then the data or question format might be asking for a different combination (e.g., direct sum), but with usual interpretation, \boxed{(D) 8} would be mathematically valid.