Consider the following. 21, 19, 33, 22, 15 Compute the population standard deviation of the numbers. (Round your answer to one decimal place.) (a) Add a nonzero constant c to each of your original numbers and compute the standard deviation of this new population. (Round your answer to one decimal place.) (b) Use the results from part (a) and inductive reasoning to state what happens to the standard deviation of a population when a nonzero constant c is added to each data item. The standard deviation increases by c. The standard deviation remains the same. The standard deviation becomes 0. The standard deviation becomes c. The standard deviation decreases by c.
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.
Consider the following.
Compute the population standard deviation of the numbers. (Round your answer to one decimal place.)
(b) Use the results from part (a) and inductive reasoning to state what happens to the standard deviation of a population when a nonzero constant c is added to each data item.
![**Consider the following:**
Numbers: 21, 19, 33, 22, 15
**Task:**
Compute the population standard deviation of the numbers. (Round your answer to one decimal place.)
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**(a)** Add a nonzero constant \( c \) to each of your original numbers and compute the standard deviation of this new population. (Round your answer to one decimal place.)
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**(b)** Use the results from part (a) and inductive reasoning to state what happens to the standard deviation of a population when a nonzero constant \( c \) is added to each data item.
- [ ] The standard deviation increases by \( c \).
- [ ] The standard deviation remains the same.
- [ ] The standard deviation becomes 0.
- [ ] The standard deviation becomes \( c \).
- [ ] The standard deviation decreases by \( c \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F82b03c70-ebcb-4dea-8d7d-49a1afe57bc5%2Fe7275dd2-1cc7-4bc5-a97f-3f4526d59fa5%2Fwwhl3e_processed.png&w=3840&q=75)
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