If a constant k is added to all values in a dataset, what happens to the mean?

If a constant k is added to all values in a dataset, what happens to the mean?

• A. The mean increases by k
• B. The mean decreases by k
• C. The mean is unchanged
• D. The mean is squared

Answer: (A)

When a constant \( k \) is added to all values in a dataset, the effect on the mean can be understood through the definition of the mean and properties of averages. The mean of a dataset is computed by summing all the values and dividing by the number of values. If you have a dataset represented as \( x_1, x_2, x_3, \ldots, x_n \), the mean \( \mu \) is calculated as: \[ \mu = \frac{x_1 + x_2 + x_3 + \ldots + x_n}{n} \] When you add a constant \( k \) to each value, the dataset transforms to \( (x_1 + k), (x_2 + k), (x_3 + k), \ldots, (x_n + k) \). The new mean \( \mu' \) of this modified dataset will be: \[ \mu' = \frac{(x_1 + k) + (x_2 + k) + (x_3 + k) + \ldots + (x_n + k)}{n} \] This simplifies to: \[ \mu'

When a constant ( k ) is added to all values in a dataset, the effect on the mean can be understood through the definition of the mean and properties of averages. The mean of a dataset is computed by summing all the values and dividing by the number of values.

If you have a dataset represented as ( x_1, x_2, x_3, \ldots, x_n ), the mean ( \mu ) is calculated as:

[

\mu = \frac{x_1 + x_2 + x_3 + \ldots + x_n}{n}

]

When you add a constant ( k ) to each value, the dataset transforms to ( (x_1 + k), (x_2 + k), (x_3 + k), \ldots, (x_n + k) ). The new mean ( \mu' ) of this modified dataset will be:

[

\mu' = \frac{(x_1 + k) + (x_2 + k) + (x_3 + k) + \ldots + (x_n + k)}{n}

]

This simplifies to:

[

\mu'