In this problem, we explore the effect on the standard deviation of adding the same constant to each data value in a data set. Consider the following data set. 13, 9, 8, 11, 10 (a) Use the defining formula, the computation formula, or a calculator to compute s. (Enter your answer to one decimal place.) (b) Add 6 to each data value to get the new data set 19, 15, 14, 17, 16. Compute s. (Enter your answer to one decimal place.) (c) Compare the results of parts (a) and (b). In general, how do you think the standard deviation of a data set changes if the same constant is added to each data value? 1)Adding the same constant c to each data value results in the standard deviation remaining the same. 2)Adding the same constant c to each data value results in the standard deviation increasing by c units. 3)Adding the same constant c to each data value results in the standard deviation decreasing by c units. 4)There is no distinct pattern when the same constant is added to each data value in a set. Which number is the answer?
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 standard deviation of adding the same constant to each data value in a data set. Consider the following data set.
(b) Add 6 to each data value to get the new data set 19, 15, 14, 17, 16. Compute s. (Enter your answer to one decimal place.)
(c) Compare the results of parts (a) and (b). In general, how do you think the standard deviation of a data set changes if the same constant is added to each data value?
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