The SD of 15 items is 6 and each item is decreased by 1, then standard deviation will be

Options

A. 5
B. 7
C. `(91)/(15)`
D. 6

Answer

To solve the problem, we need to understand the concept of standard deviation and how it is affected by changes in the data set. Here’s the step-by-step solution:

### Step 1: Understand the given data
We are given that the standard deviation (SD) of 15 items is 6.

### Step 2: Recall the effect of constant changes on standard deviation
When every item in a data set is increased or decreased by the same constant value, the standard deviation of the data set remains unchanged. This is a key property of standard deviation.

### Step 3: Apply the property to the problem
In this case, each item is decreased by 1. According to the property mentioned in Step 2, since all items are decreased by the same amount (1), the standard deviation will remain the same.

### Step 4: State the final result
Therefore, the new standard deviation after decreasing each item by 1 will still be 6.

### Final Answer:
The standard deviation will remain 6.

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