What is the value of SS (sum of squared deviations) for the following population? Population: 2, 3, 0, 5
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.
![**Question:**
What is the value of SS (sum of squared deviations) for the following population?
Population: 2, 3, 0, 5
**Explanation:**
To find the sum of squared deviations (SS), you need to:
1. Calculate the mean of the population.
2. Subtract the mean from each score to find the deviation of each score.
3. Square each deviation.
4. Sum all the squared deviations.
Let's go through each step:
1. **Mean Calculation:**
\[
\text{Mean} = \frac{(2 + 3 + 0 + 5)}{4} = \frac{10}{4} = 2.5
\]
2. **Deviation from Mean:**
- For 2: \(2 - 2.5 = -0.5\)
- For 3: \(3 - 2.5 = 0.5\)
- For 0: \(0 - 2.5 = -2.5\)
- For 5: \(5 - 2.5 = 2.5\)
3. **Squared Deviations:**
- For \(-0.5\): \((-0.5)^2 = 0.25\)
- For \(0.5\): \((0.5)^2 = 0.25\)
- For \(-2.5\): \((-2.5)^2 = 6.25\)
- For \(2.5\): \((2.5)^2 = 6.25\)
4. **Sum of Squared Deviations (SS):**
\[
\text{SS} = 0.25 + 0.25 + 6.25 + 6.25 = 13
\]
Therefore, the value of the sum of squared deviations (SS) for this population is **13**.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1639e60e-89cf-4f82-a7ff-e5a1f29b866b%2Fee74835e-422e-4b7e-af72-2e2aad7641b2%2Fii6qakg_processed.jpeg&w=3840&q=75)
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