I think it is because of outliers and how diatributions can look like, if you only know the mean.
1. A single extreme outlier can move your mean far away from where you would expect it to be, seeing all the other values.
2. If you see the mean alone, you might thing values are around that value, but not even a single value has to be anywhere cloe to the mean. For example: 1 1 1 1 9 9 9 9 → means is 5. Pathological example, but you can mix the numbers however you want and there are infinitely more examples, where the mean could mislead you.
3. The mean is part of the arguments to the formula of a Gaussian (bell shaped curve, normal distribution). The other is the standard deviation. So if you know the mean, you have already some valuable info on the bell shaped curve. You already know where its center is. That is, why giving the mean makes sense in that case.
Surely others can put it better or add lots of reasons.
I think it is because of outliers and how diatributions can look like, if you only know the mean.
1. A single extreme outlier can move your mean far away from where you would expect it to be, seeing all the other values.
2. If you see the mean alone, you might thing values are around that value, but not even a single value has to be anywhere cloe to the mean. For example: 1 1 1 1 9 9 9 9 → means is 5. Pathological example, but you can mix the numbers however you want and there are infinitely more examples, where the mean could mislead you.
3. The mean is part of the arguments to the formula of a Gaussian (bell shaped curve, normal distribution). The other is the standard deviation. So if you know the mean, you have already some valuable info on the bell shaped curve. You already know where its center is. That is, why giving the mean makes sense in that case.
Surely others can put it better or add lots of reasons.