Out of 11 births in a hospital, 5 babies weighed over 2.5 kg and 5 weighed less than 2.5 kg. What value do 2.5 represent?
First, I need to recall basic statistical terms. The question is about a central tendency measure. The options could be mean, median, mode, or range. Let's break it down.
The median is the middle value when data is ordered. Since there are 11 births, the median would be the 6th value. If 5 are above and 5 below, that suggests the 6th baby is exactly at 2.5 kg. So the median is 2.5 kg here.
Mean is the average, which would require summing all weights and dividing by 11. The problem doesn't give individual weights, so we can't calculate the mean. Mode is the most frequent value, which isn't provided here. The range is the difference between the highest and lowest, which also isn't relevant here.
So the correct answer should be the median. The user's example shows that 2.5 kg is the middle value. The other options don't fit the data given. The key point is recognizing that with an odd number of data points, the median is the middle value when sorted, and here exactly half are above and below, which aligns with the median.
**Core Concept**
This question tests understanding of **central tendency measures in statistics**, specifically the **median**. The median is the middle value in an ordered dataset, dividing the higher half from the lower half. For an odd number of observations, it is the exact middle value.
**Why the Correct Answer is Right**
In this scenario, there are 11 births (an odd number). Five babies weigh above 2.5 kg, five below 2.5 kg, and the sixth baby (the middle one when ordered) must weigh exactly 2.5 kg. This makes **2.5 kg the median**, as it divides the dataset into two equal halves. The median is less affected by outliers compared to the mean, making it a robust measure here.
**Why Each Wrong Option is Incorrect**
**Option A:** *Mean* – The mean requires summing all weights and dividing by 11. Since individual weights are not provided, 2.5 kg cannot be inferred as the mean.
**Option B:** *Mode* – The mode is the most frequently occurring value. The dataset does not indicate that 2.5 kg is the most common weight.
**Option C:** *Range* – The range is the difference between the highest and lowest values, which is unrelated to the value 2.5 kg in this context.
**Clinical Pearl / High-Yield Fact**
For an odd-numbered dataset, the median is the **(n+1)/2**th value. For even-numbered datasets, it is the average of the **n/2**th and **(n/2)+1**th values. Always remember: the median splits the data into two equal halves, while the mean is influenced by extreme values.
**Correct Answer: D. Median**