The box-and-whisker plot below represents some data set. What percentage of the data values are between 30 and 55? 10 20 30 40 50 60 70 80 90 100
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.
![**Title: Understanding Box-and-Whisker Plots**
**Jun 18, 1:00:15 PM**
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**Description:**
The question presented is as follows:
"The box-and-whisker plot below represents some dataset. What percentage of the data values are between 30 and 55?"
**Box-and-Whisker Plot Explanation:**
A box-and-whisker plot (also known as a box plot) is a graphical representation of a dataset that displays the median, quartiles, and extremes of the data. Below is the specific box-and-whisker plot provided:
```
[ |-----|-------| |-----| ]
0 10 20 30 40 50 60 70 80 90 100
```
- The left whisker starts at 10.
- The left edge of the box starts at 30.
- The line inside the box (which represents the median) is at 40.
- The right edge of the box ends at 55.
- The right whisker ends at 70.
**Analysis:**
In a box-and-whisker plot:
- The box (from 30 to 55) contains the middle 50% of the data.
- The whiskers extend to the minimum and maximum values within 1.5 IQR (Interquartile Range) from the quartiles.
**Question:**
"What percentage of the data values are between 30 and 55?"
**Answer:**
Since the box represents the middle 50% of the data:
**50% of the data values are between 30 and 55.**
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