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NECO 2023 · Paper 2 · Q12

The scores of students in a Biology test in a particular school are 12, xx, 15, 2x2x, 25, 12, 30, 15, 25, 12, 16 and 12. If the mean score is 18, find the:

  1. (a)

    value of 2x2x;

  2. (b)

    mean deviation;

  3. (c)

    standard deviation, correct to two decimal places.

Worked solution (try it first)

(a)

  1. Turn the mean into a total.
  2. There are 12 scores and the mean is 18, so they add up to 12×18=21612 \times 18 = 216.
  3. The known scores add up to 12+15+25+12+30+15+25+12+16+12=17412 + 15 + 25 + 12 + 30 + 15 + 25 + 12 + 16 + 12 = 174, and the unknown ones to x+2x=3xx + 2x = 3x.
  4. So 174+3x=216174 + 3x = 216, 3x=423x = 42 and x=14x = 14.
  5. The question asks for 2x2x: 2x=282x = 28.

(b)

  1. The scores are now 12,14,15,28,25,12,30,15,25,12,16,1212, 14, 15, 28, 25, 12, 30, 15, 25, 12, 16, 12.
  2. Their distances from the mean 18, ignoring signs, are 6,4,3,10,7,6,12,3,7,6,2,66, 4, 3, 10, 7, 6, 12, 3, 7, 6, 2, 6, which add up to 72.
  3. Mean deviation =∑∣x−xˉ∣n= \frac{\sum |x - \bar x|}{n}
    =7212= \frac{72}{12}
    =6= 6.

(c)

  1. Square each distance: 36,16,9,100,49,36,144,9,49,36,4,3636, 16, 9, 100, 49, 36, 144, 9, 49, 36, 4, 36, which add up to 524.
  2. Variance =52412≈43.67= \frac{524}{12} \approx 43.67, so the standard deviation is 43.67≈6.61\sqrt{43.67} \approx 6.61.

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