JAMB Mathematics 2011 Paper

Concept:For ungrouped data with frequencies, the median is the middle value after arranging data in order, while the range is the difference between the maximum and minimum values.Explanation:First, calculate the total number of observations: $\sum f = 1 + 4 + 3 + 8 + 2 + 5 = 23$Since $N = 23$ is odd, the median is the $\frac{23 + 1}{2} = 12$th observation.Find the cumulative frequencies:Value $0$: $1$Value $1$: $1 + 4 = 5$Value $2$: $5 + 3 = 8$Value $3$: $8 + 8 = 16$The 12th observation lies in the group where the value is $3$, because the cumulative frequency reaches $16$ at value $3$.Therefore, median $= 3$.The range is the difference between the largest and smallest values:Range $= 5 - 0 = 5$So the median and range are $3$ and $5$ respectively.Answer:$(3, 5)$Correct option is B.