Multiple choice

Calculate the standard deviation for the following distribution. Marks $(x)$ $10$ $20$ $30$ $40$ $50$ Number of students $(f)$ $4$ $3$ $6$ $5$ $2$

  1. $18.61$
  2. $24.61$
  3. $12.61$

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Mean = (40+60+180+200+100)/20 = 580/20 = 29. Variance = sum(f(x-mean)^2)/N = (4(10-29)^2 + 3(20-29)^2 + 6(30-29)^2 + 5(40-29)^2 + 2(50-29)^2)/20 = (1444+243+6+605+882)/20 = 3180/20 = 159. SD = sqrt(159) approx 12.61.

AI explanation

Calculate the mean as the sum of f * x divided by N, which is (40 + 60 + 180 + 200 + 100) / 20, giving a mean of 29. To find the variance, square the deviations from the mean, multiply by f, and sum them: 4 * 361 + 3 * 81 + 6 * 1 + 5 * 121 + 2 * 441, which equals 1444 + 243 + 6 + 605 + 882 equals 3180. The variance is 3180 / 20 equals 159, so the standard deviation is the square root of 159, which is approximately 12.61.

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