In this problem, we explore the effect on the mean, median, and mode of adding the same number to each data value. Consider the data set 2, 2, 3, 6, 10. (a) Compute the mode, median, and mean. (Enter your answers to one decimal place.) mode median mean (b) Add 7 to each of the data values. Compute the mode, median, and mean. (Enter your answers to one decimal place.) mode median mean (c) Compare the results of parts (a) and (b). In general, how do you think the mode, median, and mean are affected when the same constant is added to each data value in a set?
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
In this problem, we explore the effect on the
(a) Compute the mode, median, and mean. (Enter your answers to one decimal place.)
mode
median
mean
(b) Add 7 to each of the data values. Compute the mode, median, and mean. (Enter your answers to one decimal place.)
mode
median
mean
(c) Compare the results of parts (a) and (b). In general, how do you think the mode, median, and mean are affected when the same constant is added to each data value in a set?
-Adding the same constant c to each data value results in the mode, median, and mean decreasing by c units.
-Adding the same constant c to each data value results in the mode, median, and mean remaining the same.
-Adding the same constant c to each data value results in the mode, median, and mean increasing by c units.
-There is no distinct pattern when the same constant is added to each data value in a set.
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