Consider the given information of a data set.
Mean:62 Median:55 Mode:49
Range:46 Standard Deviation:15.5
We are asked to find the measures shown when each value of the data set increases by 14. Let's first find the measures of center and then the measures of variation.
Measures of Center
When a real number k is added to each value in a data set, the measures of center of the new data set can be found by adding k to the original measures of center. The measures of center are the mean, the median, and the mode. Therefore, we can calculate the measures for the new data set by adding 14 to each original measure.
Measure of Center
Original Data Set
+14
New Data Set
Mean
62
62 + 14
76
Median
55
55 + 14
69
Mode
49
49 + 14
63
Measures of Variation
When a real number k is added to each value in a data set, the measures of variation are the same as the original measures of variation. The measures of variation are the range and the standard deviation. With this in mind, we can now find the range and the standard deviation when the data set increases by 14.
Measure of Variation
Original Data Set
New Data Set
Range
46
46
Standard Deviation
15.5
15.5
Joining the Measures
Now we can bring the measures together to have all the new values of the measures shown.
Mean:76 Median:69 Mode:63
Range:46 Standard Deviation:15.5
