Here is the second data set. 49 84 44 89 74 26 80 39 92 49 d. What is the mean (T) of this data set? e. What is the median of this data set? f. What is the mode of this data 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.
![### Data Analysis: Calculating Mean, Median, and Mode
#### Introduction
In this exercise, we will calculate the mean, median, and mode for two sets of data. **Please show your answer to one decimal place if necessary.**
#### Data Set 1
Below is the first data set:
| 48 | 78 | 53 | 22 | 45 | 42 | 61 | 97 | 87 | 22 | 54 |
#### Steps to Calculate:
1. **Mean:** Add all numbers together and then divide by the total count of numbers.
2. **Median:** Arrange the numbers in ascending order and find the middle value.
3. **Mode:** Identify the number(s) that appear most frequently.
**Example Steps for Data Set 1:**
1. **Mean Calculation:**
- Sum of numbers: \(48 + 78 + 53 + 22 + 45 + 42 + 61 + 97 + 87 + 22 + 54\)
- Total count: 11
- Mean: Sum / Total count
2. **Median Calculation:**
- Arrange numbers in ascending order: \(22, 22, 42, 45, 48, 53, 54, 61, 78, 87, 97\)
- Median is the middle value: 53
3. **Mode Calculation:**
- Frequent number(s): 22 (since it appears twice)
Proceed with these steps to perform your calculations and record the answers appropriately. This exercise will enhance your understanding of basic statistical measures.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F07eedd0d-121f-4b38-8aa1-4108ea76d137%2F3c5e50fa-814d-4bad-aa79-10e78f524b4f%2Fbejgl2_processed.png&w=3840&q=75)
![**Data Analysis Exercise**
**Here is the second data set:**
49, 84, 44, 89, 74, 26, 80, 39, 92, 49
**d.** What is the mean (\(\bar{x}\)) of this data set?
[Answer Box]
**e.** What is the median of this data set?
[Answer Box]
**f.** What is the mode of this data set?
[Answer Box]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F07eedd0d-121f-4b38-8aa1-4108ea76d137%2F3c5e50fa-814d-4bad-aa79-10e78f524b4f%2Fj1w9kib_processed.png&w=3840&q=75)
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