If30 is added to every observation in a data set, the only one of the following that is not changed is

(a) the mean. (d) the standard deviation.

(b) the 75th percentile. (e) the minimum.

(c) the median.

Short Answer

Expert verified

The correct option is (d).

Step by step solution

01

Step 1. Given

(a) the mean.

(b) the 75th percentile.

(c) the median.

(d) the standard deviation.

(e) the minimum.

02

Step 2. Concept

The spread is controlled by the standard deviation. The curve with a higher standard deviation has a wider dispersion.

03

Step 3. Calculation

Data set = 30

The distance between values does not vary when a constant is added to each data set, and the standard deviation remains the same.

As a result, answer (d) is the proper response. When 30 is added to each observation in a data collection, the standard deviation does not change.

Hence, the only one that is not changed is the standard deviation.

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