Q.Compare the median with the arithmetic mean: state two situations where median is preferable to mean, and one genuine limitation of median that mean does not share.

Median $=Q_2=D_5=P_{50}$; the sixth decile $D_6$ is the odd one out.

The median divides the data at the 50% point. The partition values that also fall at 50% are:

• Second quartile $Q_2$ (2 of 4 parts $=50\%$),
• Fifth decile $D_5$ (5 of 10 parts $=50\%$),
• Fiftieth percentile $P_{50}$ ($50\%$). …

Median = the central value splitting ordered data into two equal halves.

When the observations are arranged in ascending (or descending) order, the median is the value of the middle item; exactly 50% of the observations fall below it and 50% above it. It is a positional average unaffected by …

Median of the 7 ordered values is the 4th one $=32$.

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Order the data and average the two central values because $n=6$ is even; the median is $13$.

This is a very-short-answer item from the Measures of Central Tendency chapter of the CHSE Odisha +2 Class-12 Business Mathematics & Statistics syllabus (aligned with the NCERT/CBSE commerce curriculum).

Step 1 — arrange the values in ascending order:

$5,\ 7,\ 12,\ 14,\ 15,\ 18$

Step 2 — count the observations: $n=6$ (even).

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The correct word is positional.

The median is the value of the middle item when the data are arranged in order. Its value is fixed by the position of the central observation, not by the numerical magnitude of every value — so it is called a positional average. (By contrast, the arithmeti …

Replace mean with median: $Q_2$ equals the median.

The quartiles divide an ordered series into four equal parts. The second quartile $Q_2$ lies exactly at the half-way point of the distribution — which is precisely the definition of the median. Hence the second quartile and the …

Median position $=\frac{n+1}{2}=\frac{12}{2}=6$th value.

The eleven values $2,4,6,\dots,22$ are already arranged in ascending order. For an odd number of observations $n=11$, the median is the middle item at position …

Ordered data: $98.01, 98.08, 98.1, 98.13, 98.42$; median is the middle value $98.1$.

Arrange in ascending order:

$98.01,\;98.08,\;98.1,\;98.13,\;98.42.$

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The correct word is positional — the median is a positional average, not a mathematical one.

Averages are of two broad kinds:

• Mathematical averages — computed using all the values through arithmetic operations: Arithmetic Mean, Geometric Mean, Harmonic Mean.
• Positional averages — located by their position in an arranged (ascending/descending) series: Median and Mode. …

Median $= 190$.

Data: $198, 205, 179, 146, 210, 186, 190$. Arrange in ascending order:

$146,\; 179,\; 186,\; 190,\; 198,\; 205,\; 210$

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Correct option: (d) 83.

Data: $72, 78, 81, 88, 92, 83, 100$. Arrange in ascending order:

$72,\; 78,\; 81,\; 83,\; 88,\; 92,\; 100.$

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