ITPEC FE Subject B October 2024 Question 5

Topic: Math & Data Science

From the answer group below, select the correct combination of answers to be inserted into A and B in the program. Here, the array index starts at 1.

Function calcGeoMean receives the array dataArray (the number of elements ≥ 1) as an argument and returns the geometric mean of values in dataArray as the return value. For the numbers a1, a2, …, an, the geometric mean is n√(a1 × a2 × ⋯ × an). Here, the pow(x, y) function returns a real value by raising x to the power of y. In the program, division is performed in data type real.

[Program]
○ real: calcGeoMean(real []: dataArray)
real: product, geomean
integer: n ← the number of elements in dataArray
integer: i
product ← 1
for (increase i from 1 to n by 1)
product ← product × dataArray[i]
endfor
geomean ← pow(A, B)
return geomean

Answer group

OptionAB

Explanation

A: product, B: 1 ÷ n — the n-th root of the product is the product raised to the power 1 ÷ n.

The loop leaves a1 × a2 × ⋯ × an in product. Since pow(x, y) computes xy, and n√x = x1/n, the base is product and the exponent is 1 ÷ n. The question states that division is done in real, so the exponent is not truncated to 0.

Check with {2, 8}: product is 16 and n is 2, so the result is 160.5 = 4, and indeed 2 × 8 = 4 × 4.

Answer (b)

Why not others:

  • •(a) — base and exponent are swapped: (1 ÷ n)product, which for the example is 0.516, about 0.000015
  • •(c) — raises the product to the n-th power instead of taking the n-th root: 162 = 256
  • •(d) — gets both arguments wrong: nproduct = 216 = 65,536

Key rule: A k-th root is the power 1 ÷ k; the exponent must be computed in real arithmetic, since integer division would turn it into 0.

Math & Data Science · AI-written, may contain errors

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