Q.Which of the following is always equal to the median of a distribution?

The median is the 50% point of a distribution, so only the partition value that also locates exactly the 50% point can equal it. …

The median divides a series exactly in half — it is the value below which 50% of observations lie. Checking each option against this 50% benchmark:

• (a) Q1 locates the 25% point ($1/4 = 25\%$) — NOT the median.
• (b) Q3 locates the 75% point ($3/4 = 75\%$) — NOT the median.
• (c) D5 locates the $5/10 = 50\%$ point — EXACTLY the median, for any dataset. …

Picking Q1 or Q3 out of a vague sense that 'quartiles are related to the median' without checking WHICH fraction of the series each option actually represents — only t …