If for a data series the value of skewness is -1, then which of the following relationship between Median (Md) and Third Quartile (Q₃) holds true?

Correct option is B

When the skewness of a data series is -1, it suggests a negatively skewed distribution. However, in some cases, even with skewness, the median (Md) and the third quartile (Q₃) may still have no significant difference, resulting in:
Md−Q3​=0
This indicates that the central value (median) is balanced relative to the upper quartile (Q₃). This relationship suggests that the skewness is mild or the negative skewness does not significantly affect the relative positioning of the median and Q₃.
Information Booster 1. Skewness:
· Positive Skewness: Mean > Median > Mode (Right skew).
· Negative Skewness: Mean < Median < Mode (Left skew).
2. Symmetrical Distribution: In a perfectly symmetrical distribution, mean = median = mode.
3. Quartiles:
· Q₁ (First Quartile): 25% of the data falls below this point.
· Q₂ (Median): 50% of the data falls below this point.
· Q₃ (Third Quartile): 75% of the data falls below this point.
4. Negative Skewness Impact:
· In a mildly negatively skewed distribution, Md - Q₃ ≈ 0.
5. Importance of Skewness:
· Skewness helps understand the shape and distribution of data.
· In skewed distributions, the median is often used as a measure of central tendency instead of the mean.
Additional Knowledge · (a) Md - Q₃ = 1: Indicates a positively skewed distribution.
· (b) Md - Q₃ = 0: Indicates a balanced relationship despite skewness.
· (c) Md - Q₃ = -1: Indicates a more noticeable negative skewness.
· (d) Md - Q₃ = -1.5: Suggests an extreme negative skewness.