Concept explainers
To find the values of Mean, Median, Mode, Range and Standard deviation when multiplied by 3 and increased by 8.
Answer to Problem 35E
Mean:
Median:
Mode:
Range:
Standard deviation:
Explanation of Solution
Given information: Mean:
Calculation:
- As a general rule, the median, mean, and mode will be changed by adding a constant to each value. However, the range, standard deviation and variance will remain the same.
- Multiplying every value by a constant, however, will multiply the mean, median, mode, range, and standard deviation by that constant, and multiply the variance (which is simply the square of the standard deviation) by the square of that constant.
When multiplied by 3 and increased by 8.
- Mean
Mean:
Now,
When multiplied by 3 and increased by 8.
So,
Mean:
Now,
Mean:
Hence,
Mean:
- Median
Median:
Now,
When multiplied by 3 and increased by 8.
So,
Median:
Now,
Median:
Hence,
Median:
- Mode
Mode:
Now,
When multiplied by 3 and increased by 8.
So,
Mode:
Now,
Mode:
Hence,
Mode:
- Range
Range:
Now,
When multiplied by 3 and increased by 8.
So,
Range:
Hence,
Range:
- Standard deviation
Standard deviation:
Now,
When multiplied by 3 and increased by 8.
So,
Standard deviation:
Hence,
Standard deviation:
Chapter 11 Solutions
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