The best interpretation of the standard deviation value of $125 in this context is that the amount shoppers spent typically varies by about $125 from the mean.
To understand this interpretation, let's break it down step by step:
1. The standard deviation measures the variability or spread of a set of data. In this case, it represents how much the amounts shoppers spent deviate or differ from the average spending.
2. The average spending is represented by the mean. For example, if the mean spending is $500, the standard deviation of $125 suggests that shoppers' spending typically varies by about $125 above or below this mean.
3. It's important to note that the standard deviation does not provide specific information about the percentage of amounts above or below a certain value, such as $125. So, the statement "Fifty percent of the amount shoppers spent is above $125" is not accurate.
4. The statement "The middle half of the amount shoppers spent has a range that is $125 wide" is also not accurate. The middle half of the amounts spent would be represented by the interquartile range, which is a different measure of variability.
5. Lastly, the statement "The difference between the largest and smallest amounts shoppers spent was $125" does not provide any information about the variability or spread of the data. It only focuses on the range, which is the difference between the largest and smallest values.
Therefore, the interpretation that the amount shoppers spent typically varies by about $125 from the mean is the best one based on the given information. This suggests that there is a certain level of variability in shoppers' spending patterns.