The numbers of students in the 8 schools in a district are given below. (Note that these are already ordered from least to greatest.) 158, 252, 258, 286, 377, 419, 425, 449 Send data to calculator Suppose that the number 449 from this list changes to 529. Answer the following. (a) What happens to the median? OIt decreases by It increases by U O It stays the same. (b) What happens to the mean? O It decreases by O It increases by U O It stays the same. Exmlanation Check
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.
 - **Send data to calculator**
Suppose that the number 449 from this list changes to 529. Answer the following questions:
1. **What happens to the median?**
- [ ] It decreases by
- [ ] It increases by
- [ ] It stays the same.
2. **What happens to the mean?**
- [ ] It decreases by
- [ ] It increases by
- [ ] It stays the same.
 - **Explanation**
 - **Check**
#### Explanation:
In this example, we are examining how changing a value in a data set impacts the mean and median. The data set provided consists of the number of students from 8 different schools, ordered from smallest to largest. The initial data points are: 158, 252, 258, 286, 377, 419, 425, and 449.
If we change the last value of 449 to 529:
- **Mean**: The mean is calculated by summing all numbers in the data set and dividing by the number of values. Changing 449 to 529 increases the overall sum, thereby increasing the mean.
- **Median**: The median is the middle value of a data set when it is ordered. For an even number of data points, the median is the average of the two middle numbers. Changing 449 to 529 does not affect the middle numbers, so the median remains the same.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5c408b24-72ca-4f3d-857b-96deb6fc7977%2F8ae29f67-efa9-4f20-b369-baf753d3c54d%2F0eh57n_processed.jpeg&w=3840&q=75)
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
