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WAEC 2018 · Paper 2 · Q12

  1. (a)
    Candidate A B C D E F G H I J
    Test 1 10 6 4 5 3 1 8 9 7 2
    Test 2 10 9 3 4 2 1 5 6 8 7

    The ranks of ten candidates in two tests are as shown. Calculate the Spearman's rank correlation coefficient (4 d.p.).

  2. (b)

    A committee of three men and two women is to be formed from four men and six women. How many different committees can be formed if: (i) there are no restrictions; (ii) a particular man and a particular woman cannot serve together on the same committee?

    Separate values with commas, e.g. 3, −2

Worked solution (try it first)

(a)

  1. The scores are already ranks.
  2. dd = Test 1 rank − Test 2 rank: 0,−3,1,1,1,0,3,3,−1,−50, -3, 1, 1, 1, 0, 3, 3, -1, -5.
  3. ∑d2=0+9+1+1+1+0+9+9+1+25\sum d^2 = 0 + 9 + 1 + 1 + 1 + 0 + 9 + 9 + 1 + 25
    =56= 56.
  4. ρ=1−6∑d2n(n2−1)\rho = 1 - \dfrac{6\sum d^2}{n(n^2 - 1)}
    =1−6×5610×99= 1 - \dfrac{6 \times 56}{10 \times 99}
    =1−336990= 1 - \dfrac{336}{990}
    ≈0.6606\approx 0.6606.

(b)(i)

  1.  4C3×6C2=4×15\,{}^4C_3 \times {}^6C_2 = 4 \times 15
    =60= 60 committees.

(ii)

  1. Committees with both the man and the woman: the other 2 men from 3 and the other woman from 5,  3C2×5C1=15\,{}^3C_2 \times {}^5C_1 = 15.
  2. So 60−15=4560 - 15 = 45 committees keep them apart.

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