Four graphs of different data sets are shown. Which data set has the greatest standard deviation?

Question

A.
The graph of data set A shows 50 on the horizontal axis, has a normal symmetrical bell curve and the highest frequency is represented by a dashed line at 50.

B.
The graph of data set B shows 50 on the horizontal axis, has a wide symmetrical bell curve and the highest frequency is represented by a dashed line at 50.

C.
The graph of data set C shows 50 on the horizontal axis, has a symmetrical bell curve and the highest frequency is represented by a dashed line which is to the right of 50.

D.
The graph of data set D shows 50 on the horizontal axis, has a symmetrical bell curve and the highest frequency is represented by a dashed line which is to the left of 50.

Answer 1

To determine which data set has the greatest standard deviation based on the descriptions of the graphs, we can analyze the characteristics:

• Standard Deviation Concept: The standard deviation is a measure of the amount of variation or dispersion in a set of values. A larger standard deviation indicates that the values are spread out more widely around the mean.

• Graph Characteristics:

  • A: Normal bell curve, tightly peaked around the mean (50). This suggests a lower standard deviation.
  • B: Wide symmetrical bell curve, indicating a larger spread of data points around the mean (50). This suggests a higher standard deviation than A.
  • C: Symmetrical bell curve with the highest frequency to the right of 50, indicating that the data set is shifted right but still relatively tight. It does not imply a larger spread compared to B.
  • D: Similar to C in shape but shifted to the left; this suggests a close relation to the mean but may not indicate such a high spread as B.

Given the comparison, data set B, which has a wide symmetrical bell curve, would have the greatest standard deviation because its values are more spread out around the mean of 50 compared to the other datasets. Thus, the answer is:

B.