In a positively shewed curve, true statement is?
**Core Concept**
A positively skewed curve is a type of distribution in statistics, characterized by a longer tail on the right side. This indicates that the values are concentrated on the lower end of the spectrum, with a few extreme values on the higher end.
**Why the Correct Answer is Right**
In a positively skewed curve, the mean is typically greater than the median. This is because the extreme values on the higher end of the distribution pull the mean upwards, resulting in a higher mean. The median, on the other hand, is a more robust measure of central tendency, less affected by extreme values. The mode, which is the most frequently occurring value, is often lower than the median.
**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because in a positively skewed curve, the mode is not necessarily lower than the median. The mode is the most frequently occurring value, which may or may not be lower than the median.
**Option B:** This option is incorrect because in a positively skewed curve, the mean is not necessarily lower than the median. As explained earlier, the mean is typically greater than the median.
**Option D:** This option is incorrect because in a positively skewed curve, the median is not necessarily higher than the mean. The median is a more robust measure of central tendency, less affected by extreme values.
**Clinical Pearl / High-Yield Fact**
When analyzing a distribution, it's essential to consider the shape of the curve. A positively skewed curve may indicate the presence of outliers or extreme values, which can affect the mean but not the median.
**Correct Answer: C. The mean is greater than the median.**