Question

1. comparing sd the parallel dotplots show the lengths (in millimeters) of a sample of 11 nails produced by each of two machines. which distribution has the larger standard deviation? justify your answer.

Explanation:

Step1: Recall SD concept

Standard deviation (SD) measures data spread. More spread out data has larger SD.

Step2: Analyze Machine A's data

Machine A's dots are more spread out (e.g., from leftmost to rightmost dot, the range is larger, and dots are less clustered around a central value).

Step3: Analyze Machine B's data

Machine B's dots are clustered more closely around values (e.g., most dots are near 68, 69, 71, 72 but with less spread between extreme values compared to A).

Step4: Compare spreads

Since Machine A's data points are more dispersed (wider range, less clustering) than Machine B's, it has a larger standard deviation.

Answer:

Machine A has the larger standard deviation. Justification: Standard deviation measures the spread of data. Machine A’s nail length data points are more spread out (less clustered, wider range of values) compared to Machine B’s data, which is more clustered around specific lengths. A more spread - out distribution has a larger standard deviation.