Step 1 :Given two normally distributed sets of data, Data Set A and Data Set B. Data Set A has a mean of 15 and a standard deviation of 5. Data Set B also has a mean of 15 but a standard deviation of 1.
Step 2 :Sketch the normal curve for each set of data. The mean determines the center of the distribution, while the standard deviation determines the spread of the distribution.
Step 3 :For Data Set A, the curve is centered at the mean of 15 and has a wider spread due to its larger standard deviation of 5.
Step 4 :For Data Set B, the curve is also centered at the mean of 15 but has a narrower spread due to its smaller standard deviation of 1.
Step 5 :From the sketches, it can be observed that both curves are centered at the same point since they have the same mean. However, Data Set A has a wider spread due to its larger standard deviation, while Data Set B has a narrower spread due to its smaller standard deviation.
Step 6 :\(\boxed{\text{Final Answer: The mean determines the center of the distribution, while the standard deviation determines the spread of the distribution. A larger standard deviation results in a wider spread, and a smaller standard deviation results in a narrower spread.}}\)