Explanation:

Mean and Standard Deviation:
To understand the answer to this question, we first need to understand the concepts of mean and standard deviation. The mean is the average of a set of values and is a measure of central tendency. The standard deviation is a measure of the dispersion or spread of the values from the mean. It tells us how much the values deviate from the mean.

Values close to the mean:
When we say values close to the mean, we are referring to values that are within one standard deviation from the mean. In a normal distribution, approximately 68% of the values fall within one standard deviation of the mean.

Standard Deviations:
Now, let's analyze the given options:

a) Big:
If the standard deviation is big, it means that the values are spread out or dispersed from the mean. In this case, there will be a significant number of values that are far from the mean. Therefore, it is not correct to say that values close to the mean have a big standard deviation.

b) Small:
If the standard deviation is small, it means that the values are closely packed around the mean. In this case, there will be a small number of values that are far from the mean. Therefore, it is correct to say that values close to the mean have a small standard deviation.

c) Moderate:
If the standard deviation is moderate, it means that the values are moderately spread out from the mean. In this case, there will be a moderate number of values that are far from the mean. Therefore, it is not correct to say that values close to the mean have a moderate standard deviation.

d) None:
This option is not correct since the standard deviation is a measure of the spread of values from the mean. It is not possible to have no standard deviation.

Therefore, the correct answer is option 'b' - small. Values close to the mean have a small standard deviation because they are closely packed around the mean.