Question

1. which of the following distributions has the smallest standard deviation?

Explanation:

Step1: Understand the concept of standard deviation

Standard deviation measures the spread of data. A smaller standard deviation means data is more clustered around the mean.

Step2: Analyze each histogram

• Histogram (a): Data is spread out with lower frequencies in the middle range.
• Histogram (b): Uniform distribution (all bars have the same height). Data is spread evenly across the range.
• Histogram (c): Data is spread out with a relatively flat - topped distribution.
• Histogram (d): Data is clustered more closely around the middle values (higher frequencies near the center).

Since the data in histogram (d) is more concentrated around a central region compared to the other histograms, it has the smallest spread.

Answer:

(d)