The systolic blood pressure of 10 individuals was measured. The mean and median values were calculated to be 130 mmHg and 140 mmHg respectively. What is the shape of the frequency distribution curve?
**Core Concept**
The shape of a frequency distribution curve is determined by the relationship between the mean, median, and mode of a dataset. In a normal distribution, these three measures are equal. However, when the mean is less than the median, it indicates a skewness in the distribution.
**Why the Correct Answer is Right**
In this scenario, the mean systolic blood pressure is 130 mmHg, while the median is 140 mmHg. This discrepancy suggests that the dataset is skewed to the left, as the mean is less than the median. This type of skewness is known as negative skewness. To understand why, consider that a few individuals in the dataset may have extremely high systolic blood pressures, pulling the mean down. This would result in a negatively skewed distribution, where the majority of values are concentrated on the right side of the distribution, with a few extreme values on the left.
**Why Each Wrong Option is Incorrect**
**Option A:** A symmetrical distribution would have equal mean and median values, which is not the case here. The mean and median values differ, indicating a lack of symmetry.
**Option B:** A bimodal distribution would have two distinct peaks, indicating that the dataset is composed of two distinct populations. However, the given information does not suggest the presence of two distinct populations.
**Option C:** A positively skewed distribution would have a mean greater than the median, which is the opposite of what is observed in this scenario.
**Clinical Pearl / High-Yield Fact**
When interpreting the shape of a frequency distribution curve, it's essential to consider the relationship between the mean, median, and mode. A negatively skewed distribution, like the one in this scenario, can indicate the presence of extreme values or outliers in the dataset.
**✓ Correct Answer: D. Negatively skewed distribution**