For a symmetrical distribution, we have:
mean = median = mode
For a symmetrical distribution (such as the normal distribution), the data is evenly distributed around the central value. The left and right halves of the distribution are mirror images of each other.
Because of this perfect symmetry, the three measures of central tendency coincide at the same point:
\(\text{Mean} = \text{Median} = \text{Mode}\)
In contrast:
- For a positively skewed distribution: \(\text{Mean} > \text{Median} > \text{Mode}\)
- For a negatively skewed distribution: \(\text{Mean} < \text{Median} < \text{Mode}\)
Hence, the correct answer is mean = median = mode.
Similar Questions
If for a group of 20 items, ∑x = 1452, ∑x² = 144280 and mode = 63.7, then Pearsonian coefficient of skewness is equal to:
Positive skewness means that the frequencies in the distribution are spread:
Which of the following is an absolute measure of skewness?
For a negatively skewed and platykurtic distribution:
If the distribution is negatively skewed then:
If median = 45, mean = 39.27, SD = 22.81, then the coefficient of Skewness is:
If Mean > Median > Mode, then distribution is:
For a data set, the following information is obtained. If Q1 = 62, Q2 = 142 and Q3 = 195, then Bowley’s coefficient of skewness is:
In case of a moderately skewed frequency distribution, the mean is 50 and the median is 53. If the coefficient of variation is 20%, then the coefficient of skewness is:
The mode of the given data set is 12. The sum of the frequencies on both sides of mode are 16. The skewness:
Important Questions from Measures of skewness
Which one of the following statements is true?
If for a group of 20 items, ∑x = 1452, ∑x² = 144280 and mode = 63.7, then Pearsonian coefficient of skewness is equal to:
Positive skewness means that the frequencies in the distribution are spread:
Which of the following is an absolute measure of skewness?
For a negatively skewed and platykurtic distribution:
