The table shows the numbers of cases of Corona Virus registered in Uganda between March, 2020 and June, 2021. Draw a frequency distribution table, a graph of cumulative frequencies, and estimate the median.

Step 1: Determine the total number of cases.
Add the frequencies:
$14 + 15 + 20 + 14 + 9 + 5 + 2 + 1 + 1 = 81$
Total cases, $N = 81$.

Step 2: Identify the median position.
The median is the $\frac{N+1}{2}$th value:
$\frac{81 + 1}{2} = 41$
The 41st case.

Step 3: Construct the cumulative frequency (cf) table using upper class boundaries.
Classes: $0-9$, $10-19$, $20-29$, $30-39$, $40-49$, $50-59$, $60-69$, $70-79$, $80+$.
Upper boundaries: $10$, $20$, $30$, $40$, $50$, $60$, $70$, $80$, $90$.

Step 4: Draw the cumulative frequency polygon (ogive).
Plot points: $(10,14)$, $(20,29)$, $(30,49)$, $(40,63)$, $(50,72)$, $(60,77)$, $(70,79)$, $(80,80)$, $(90,81)$.
Join with straight lines.

Step 5: Locate the median on the graph.
Draw horizontal line at cf $= 41$.
It intersects the line segment from $(20, 29)$ to $(30, 49)$.

Step 6: Calculate the median value.
Formula for intersection:
$x = L + \frac{M - cf_{prev}}{ cf - cf_{prev} } \times w$
where $L = 20$ (upper boundary of previous class),
$M = 41$ (median position),
$\text{cf}_{prev} = 29$,
$\text{cf} - cf_{prev} = 49 - 29 = 20$,
$w = 30 - 20 = 10$ (class width).

Substitute:
$x = 20 + \frac{41 - 29}{20} \times 10$
$x = 20 + \frac{12}{20} \times 10$
$x = 20 + 0.6 \times 10$
$x = 20 + 6 = 26$

(c) Explanation: The ogive is plotted with cumulative frequencies against upper class boundaries. The horizontal line at cf $= 41$ intersects the ogive between upper boundaries $20$ and $30$. The x-coordinate of the intersection gives the estimated median of $26$ cases.

26