Constant Changes to Data $aX+b$
Adding a Constant to all Data Values
Imagine that the app rating system that was out of 10 is going to be changed to be out of 20.To convert the data, each of the previous rating scores will be increased by 8.
Fill in the new rating scores.
| Data $x$ |
$5$ | $6$ | $6$ | $6$ | $6$ | $6$ | $7$ | $7$ | $7$ | $7$ | $7$ | $7$ | $7$ | $7$ | $7$ | $8$ | $8$ | $8$ | $8$ | $8$ | $9$ |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| $x+8$ |
Mode =
Mean =
Median =
Range =
Interquartile Range =
Standard Deviation =
Variance =
Example 2
Mode =
Mean =
Median =
Range =
Interquartile Range =
Standard Deviation =
Variance =
If all data values are increased by $b$, the mode, mean and median
,
the standard deviation , and the variance .
the standard deviation , and the variance .
Multiplying a Constant to all Data Values
Imagine that the app rating system that was out of 10 is going to be changed to be out of 20.To convert the data, each of the previous rating scores will be multiplied by 2.
Fill in the new rating scores.
| Data $x$ |
$5$ | $6$ | $6$ | $6$ | $6$ | $6$ | $7$ | $7$ | $7$ | $7$ | $7$ | $7$ | $7$ | $7$ | $7$ | $8$ | $8$ | $8$ | $8$ | $8$ | $9$ |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| $2x$ |
Mode =
Mean =
Median =
Range =
Interquartile Range =
Standard Deviation =
Variance =
Example 2
Mode =
Mean =
Median =
Range =
Interquartile Range =
Standard Deviation =
Variance =
If all data values are multiplied by $a$, the mode, mean and median
,
the standard deviation , and the variance .
the standard deviation , and the variance .