When the mean of a normal distribution is shifted, what happens?

When the mean of a normal distribution is shifted, what happens?

• A. The central tendency remains the same
• B. The position of the central line through the curve shifts
• C. The spread of the distribution narrows
• D. The standard deviation becomes zero

Answer: (B)

When the mean of a normal distribution is shifted, the position of the central line through the curve shifts. This is because the mean represents the average value of the data set and acts as the center point of the distribution. In a normal distribution, the curve is symmetric around the mean, so changing the mean directly moves the entire curve left or right on the horizontal axis without changing its shape. The spread of the distribution, which is defined by the standard deviation, remains constant unless specifically altered. This means that although the center moves, the width of the curve—indicating how much the data values deviate from the mean—does not change. Consequently, the characteristics of the distribution related to spread and variability remain intact. Thus, the effect of shifting the mean is solely on the location of the central tendency, aligning perfectly with the assertion that the position of the central line through the curve shifts.

When the mean of a normal distribution is shifted, the position of the central line through the curve shifts. This is because the mean represents the average value of the data set and acts as the center point of the distribution. In a normal distribution, the curve is symmetric around the mean, so changing the mean directly moves the entire curve left or right on the horizontal axis without changing its shape.

The spread of the distribution, which is defined by the standard deviation, remains constant unless specifically altered. This means that although the center moves, the width of the curve—indicating how much the data values deviate from the mean—does not change. Consequently, the characteristics of the distribution related to spread and variability remain intact. Thus, the effect of shifting the mean is solely on the location of the central tendency, aligning perfectly with the assertion that the position of the central line through the curve shifts.