In a symmetric distribution, the mean, median, and mode are equal.

In a symmetric distribution, the mean, median, and mode are equal.

• A. Mean = Median but not Mode
• B. Mean = Median = Mode
• C. Mode = Median but not Mean
• D. All three are different

Answer: (B)

In a symmetric distribution, the center value acts as the balance point of the data. The median is the middle value, so half the observations lie on each side of that central point, placing the median right at the center. The mean is the balance point of all values; with perfect symmetry, the deviations on one side cancel the deviations on the other, pulling the mean to the same central value. The mode is the most frequent value, and in a symmetric unimodal distribution, the highest frequency sits at the center, so the mode also equals that central value. Put together, all three measures coincide at the center. Keep in mind that if the distribution is symmetric but multimodal (having multiple peaks), the mode might not be a single value at the center, but in the typical unimodal, symmetric case, they are all equal.

In a symmetric distribution, the center value acts as the balance point of the data. The median is the middle value, so half the observations lie on each side of that central point, placing the median right at the center. The mean is the balance point of all values; with perfect symmetry, the deviations on one side cancel the deviations on the other, pulling the mean to the same central value. The mode is the most frequent value, and in a symmetric unimodal distribution, the highest frequency sits at the center, so the mode also equals that central value. Put together, all three measures coincide at the center. Keep in mind that if the distribution is symmetric but multimodal (having multiple peaks), the mode might not be a single value at the center, but in the typical unimodal, symmetric case, they are all equal.