Statistics

Step 1: Organize the data in increasing order.
The given values are: Arranging these values in increasing order: Step 2: Find the median.
Since there are 8 values (even number of values), the median is the average of the 4th and 5th values in the ordered list. The 4th value is and the 5th value is . The median is given by the average of these two values: Step 3: Conclusion.
Thus, the median is , corresponding to option (4).

Step 1: Understanding Gaussian Distribution.
In a normal (Gaussian) distribution, the shape of the curve is determined by the mean (central location) and the standard deviation (spread or width) of the distribution. The larger the standard deviation, the wider and flatter the distribution curve will be. Conversely, the smaller the standard deviation, the narrower and taller the curve becomes.
Step 2: Impact of changing spread and height.
Decreasing the spread refers to reducing the standard deviation, which leads to a more concentrated distribution around the mean.
Increasing the height of the curve corresponds to a taller distribution, which directly happens when the standard deviation is reduced, as the probability density increases near the mean.
Step 3: Conclusion.
When you decrease the spread (standard deviation) of a normal distribution, the curve becomes narrower, and its height increases. This is because the area under the curve remains constant (total probability = 1), so a narrower distribution leads to a higher peak. Therefore, decreasing the spread results in a smaller value of standard deviation.