Suppose that each number in a data set is decreased by 5. How is the median affected?
1. It is unchanged.
2. It is decreased by 5.
3. You can't tell because it depends on the values in the original data.
the mean is the total divided by the count. So, the original mean is
M = (v1+v2+...+vn)/n
The new mean is
(v1-5 + v2-5 + ... + vn-5)/n
= (v1+v2+...+vn - 5n)/n
= (v1+v2+...+vn)/5 - 5n/n
= M-5
is the answer 2(it decreased by 5)
To determine how the median is affected when each number in a data set is decreased by 5, we first need to understand what the median represents. The median is the middle value in a data set when the values are arranged in ascending or descending order.
When each number in a data set is decreased by 5, the relative order of the values in the data set remains the same. However, the entire data set is shifted downward by a constant value of 5. This means that all the individual values in the data set are reduced by 5 units.
Now, let's consider the given options:
1. It is unchanged: This option is incorrect because if each number is decreased by 5, the values are shifted downward, causing the median to change.
2. It is decreased by 5: This option is also incorrect because when each number is decreased by 5, the median will not be decreased by exactly 5 units. The exact change in the median will depend on the values in the original data set.
3. You can't tell because it depends on the values in the original data: This option is correct. The change in the median depends on the specific values in the original data set. If the initial data set had a large range of values, the median might change significantly. On the other hand, if the original data set was relatively small, the median might change only slightly.
In summary, the correct option is 3. You can't tell because it depends on the values in the original data.