ITPEC FE Subject B October 2024 Question 14

Topic: Math & Data Science

From the answer group below, select the correct answer to be inserted into blank in the description. Here, the array indexes start at 1.

The function summarize receives the array sortedData sorted in ascending order and returns five values that characterize the array. The array sortedData must have at least one element. The summarize calls the findRank with two arguments, sortedData and q.
When the function summarize is called as summarize({0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1}), the return value is blank.

[Program]
○ real: findRank(real []: sortedData, real: q)
integer: j
j ← floor(q × (the number of elements in sortedData - 1))
// floor returns the closest integer less than or equal to a given
// number, e.g. floor(7.75) returns 7.
return sortedData[j + 1]
○ real []: summarize(real []: sortedData)
real []: rankData ← {} /* array with 0 elements */
real []: q ← {0, 0.25, 0.5, 0.75, 1}
integer: i
for (increase i from 1 to the number of elements in q by 1)
add the return value of findRank(sortedData, q[i]) to the end of rankData
endfor
return rankData

Answer group

Explanation

{0.1, 0.3, 0.5, 0.7, 1} — findRank returns the element at position floor(q × (n − 1)) + 1, giving the minimum, the quartiles, the median and the maximum.

sortedData has 10 elements, so n - 1 = 9. Each call computes j as the floor of q × 9 and returns sortedData[j + 1]:

q[i]q × 9jpositionvalue
00010.1
0.252.25230.3
0.54.5450.5
0.756.75670.7
199101

Each value is added to the end of rankData in that order.

Answer (e)

Why not others:

  • •(a) — the first five elements: that is j from q × 4, using the 5 elements of q instead of the 10 of sortedData
  • •(c) — reads sortedData[j] without the + 1, which gives 0.2, 0.4, 0.6 and 0.9 for the last four (and position 0, outside the array, for q = 0)
  • •(f) — differs only at q = 0.75: 0.8 is position 8, which needs j = 7, rounding 6.75 up instead of taking the floor
  • •(b) and (d) — the last value is not 1, yet q = 1 gives j = 9, position 10, the maximum
  • •(g) and (h) — the middle value is 0.6 or 0.7, yet the floor of 4.5 is 4, position 5, value 0.5

Key rule: A formula that yields an offset from 0 needs + 1 when indexes start at 1; trace the extremes (q = 0 and q = 1) first to catch off-by-one errors.

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

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