9.8.6 Bar Graph: GATE Civil 2022 Set 1 | GA Question: 8 The above frequency chart shows the frequency distribution of marks obtained by a set of students in an exam. From the data presented above, which one of the following is CORRECT? A. mean > mode > median B. mode > median > mean C. mode > mean > median D. mode > mean > median

GATE 2022 · General Aptitude · Bar Graph · medium

Answer: For the given left-skewed frequency distribution: mode > median > mean. Answer: B. mode > median > mean.

1. Identify the shape of the distribution from the chart: From the frequency chart: bars are tallest toward the right (higher marks) and the distribution has a longer tail stretching to the left (lower marks). This is a LEFT-SKEWED (negatively skewed) distribution.
2. Apply the skewness rule for mean, median, mode: For a left-skewed distribution: Mode is at the peak (highest bar on right side, highest marks region). Median is the middle value of all data, slightly to the left of mode. Mean is pulled further left by the long tail of low-scoring students. Therefore: mode > median > mean.
3. Match to answer choices: Option A: mean > mode > median — this is NOT correct (mean is smaller, not larger). Option B: mode > median > mean — CORRECT for left-skewed distributions. Options C and D both have mean between mode and median, which does not match left-skew.