Practice30Create account

Twelve readings, already in ascending order, are 5, 8, 11, 13, 14, 18, 21, 24, 27, 30, 34, 41. Taking the median of the lower six as Q1 and the median of the upper six as Q3, which list gives the five-number summary (minimum, Q1, median, Q3, maximum)?

Competition practiceData & Probability
  • A5, 12, 19.5, 28.5, 41
  • B5, 11, 19.5, 30, 41
  • C5, 12, 18, 28.5, 41
  • D5, 14, 19.5, 27, 41

Step-by-Step Solution

The extremes are 5 and 41. With twelve readings the median is the mean of the 6th and 7th, (18 + 21)/2 = 19.5. The lower half is 5, 8, 11, 13, 14, 18, and being six values its median is again a mean of a middle pair, (11 + 13)/2 = 12; the upper half 21, 24, 27, 30, 34, 41 gives (27 + 30)/2 = 28.5. So the summary is 5, 12, 19.5, 28.5, 41. Picking single values at the 3rd and 10th places instead of averaging pairs gives 11 and 30; taking the 6th reading 18 as the median forgets that an even count has no single middle; and 14 and 27 come from counting the quartile positions from the wrong end of each half.
Answer: A) 5, 12, 19.5, 28.5, 41

Master this topic in 30 minutes a day.

Don't just memorise the answer — build a daily practice habit.

Practice 5 Similar Questions Free →

All Data & Probability practice questions

More Data & Probability practice

A team of 4 is chosen at random from the 9 students of a club, and then one of the four…A flight leaves Dubai at 21:10 local time and lands in Delhi at 02:15 the next morning,…Every employee of a firm is given the same flat raise of ₹1,500 a month. Before the…The five digits of 12345 are shuffled at random to make a new five-digit number, every…The scores of 50 candidates are given as a 'less than' table — less than 10: 4, less…