Compute the mean and the median of the raw data in (1) above. Based solely on the relationship between the mean and the median, would you say that the distribution of scores is symmetrical, negatively skewed, or positively skewed? b. Transform the data in (1) above by subtracting the mean that you computed in (2) from each score. Report the resulting set of transformed scores. Compute the mean of this set of transformed scores. (Hint: If you start with N=5 scores in (1), you should get 5 transformed scores for (3) -- one for each of the original 5 scores in (1).) c. Square each of the transformed scores that you obtained in (3). Compute the mean of these squared scores. d. List all possible samples of size n=3 that you can obtain from the raw data you reported in (1) above. For each sample of size n=3 that you listed, compute the mean of the sample. What is the mean of these sample means.
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.
(1) Raw data: { 5 5 5 6 7 }
a. Compute the
b. Transform the data in (1) above by subtracting the mean that you computed in (2) from each score. Report the resulting set of transformed scores. Compute the mean of this set of transformed scores.
(Hint: If you start with N=5 scores in (1), you should get 5 transformed scores for (3) -- one for each of the original 5 scores in (1).)
c. Square each of the transformed scores that you obtained in (3). Compute the mean of these squared scores.
d. List all possible samples of size n=3 that you can obtain from the raw data you reported in (1) above. For each sample of size n=3 that you listed, compute the mean of the sample. What is the mean of these sample means.
(Hint: there is a total of 10 ways to choose samples of size n=3 from the N=5 scores you report in (1). So you should get 10 sample means -- one for each of the samples of size n=3 that you list.)
Provided data is; 5, 5, 5, 6, 7
a. Mean of the data can be calculated as:
For odd ‘n’ median can be calculated as:
Mean of the raw data is 5.6 and median is 5.
From mean and median of the raw data set, it can be concluded that data is positively skewed since median(5) < mean(5.6).
b. Transforming data by subtracting mean from each observation,
New data set is -0.6, -0.6, -0.6, 0.4, 1.4.
Mean of the transformed data is:
c. square of each transformed data is:
|
x |
-0.6 |
-0.6 |
-0.6 |
0.4 |
1.4 |
|
x2 |
0.36 |
0.36 |
0.36 |
0.16 |
1.96 |
Mean of squared data is:
Mean of squared data is 0.64.
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