Respuesta :
Considering the concepts of the statistical measures, it is found that when 5 is added to each measure:
- The mean and the median are increased by 5.
- The standard deviation remains constant.
- The iqr remains constant.
What are the mean and the standard deviation of a data-set?
- The mean of a data-set is given by the sum of all values in the data-set, divided by the number of values.
- The standard deviation of a data-set is given by the square root of the sum of the differences squared between each observation and the mean, divided by the number of values.
Hence, adding 5 to each observation, 5 will be added to the mean. For the standard deviation, however, the sum of the differences squared will remain constant, hence the standard deviation will also remain constant.
What are the median and the interquartile range of a data-set?
- The median of the data-set separates the bottom half from the upper half, that is, it is the 50th percentile.
- The first quartile is the median of the first half of the data-set.
- The third quartile is the median of the second half of the data-set.
- The IQR is the difference of the third quartile by the first quartile.
With the change, 5 will be added to each the median and the quartiles. For the subtraction on the IRQ, however, the is added then subtracted, hence it remains constant.
More can be learned about statistical measures at https://brainly.com/question/24732674
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