Find the range and standard deviation for the data items in the histogram below. 5 4 Frequency
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.
![**Find the range and standard deviation for the data items in the histogram below.**
In the histogram provided:
- The x-axis represents data values in intervals: 0-10, 10-20, 20-30, 30-40, 40-50, 50-60, 60-70.
- The y-axis represents frequency, ranging from 0 to 5.
**Frequency Distribution:**
- Interval 0-10: Frequency = 0
- Interval 10-20: Frequency = 2
- Interval 20-30: Frequency = 5
- Interval 30-40: Frequency = 5
- Interval 40-50: Frequency = 2
- Interval 50-60: Frequency = 0
- Interval 60-70: Frequency = 5
**Range Calculation:**
The range is the difference between the maximum and minimum data values. Here, it is the interval maximum (70) minus the interval minimum (10), considering non-zero frequencies:
Range = 70 - 10 = 60
**Standard Deviation Calculation:**
To calculate the standard deviation:
1. Calculate the mean of the data.
2. Subtract the mean from each data value, square the result, and average those squared differences.
3. Take the square root of this average.
*Round the standard deviation to two decimal places if needed.*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa372cc8e-6670-44e7-851f-ddc372b7bba5%2F83fffe1e-70d2-46ba-9428-380140b6b1f7%2Fikuno5c_processed.png&w=3840&q=75)
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