Question

each histogram has the same mean value. which histogram would depict a greater standard deviation? images: 1 (yellow histogram), 2 (purple histogram), 3 (orange: you can not determine with the information provided.)

Explanation:

Step1: Recall standard deviation concept

Standard deviation measures the spread of data from the mean. Data with values more spread out (wider distribution) has a greater standard deviation.

Step2: Analyze the histograms

• Histogram 1: Data seems more clustered around the center (taller middle bars, shorter outer bars).
• Histogram 2: Data has taller bars at the extremes (left and right) and shorter in the middle, meaning values are more spread out from the mean.

Answer:

Histogram 2 (the purple - colored histogram) would depict a greater standard deviation.