What is the effect on the mean, median, mode, IQR, and range of each data value is increased by 3?

Since the mean is dependent on all values, it is increased by three.

Since the median is the middle term, it is increased by three, just as all other values are increased by three.

The underlying value increases by 3, which also causes the mode, if it exists, to increase by 3.

Since IQR is equal to the first quartile minus the third quartile, and both of these quartiles increase by three, IQR remains constant.

Because range is the difference between the highest and lowest value, which both increase by three, it remains constant.

Increasing each data value in a dataset by 3 will have the following effects:

1. Mean: The mean will increase by 3 because the sum of all values increases by 3 times the number of values, and when divided by the total number of values, the increase will reflect in the mean.

2. Median: The median will also increase by 3 if the dataset has an odd number of values. If the dataset has an even number of values, the median will remain the same if all values are increased by the same amount.

3. Mode: The mode will remain unchanged as long as no values cross over to become the most frequent value due to the increase. If a value increases to become the most frequent, then that value will become the new mode.

4. Interquartile Range (IQR): The IQR is the difference between the third quartile (Q3) and the first quartile (Q1). If all values are increased by 3, both Q3 and Q1 will increase by 3, resulting in an increase in the IQR by 3.

5. Range: The range, which is the difference between the maximum and minimum values, will increase by 3 since both the maximum and minimum values increase by 3.

In summary, increasing each data value by 3 will uniformly shift the mean, median, third quartile, first quartile, and maximum and minimum values upwards by 3 units. The mode will remain the same unless a value crosses over to become the most frequent due to the increase.