Suppose that your statistics professor returned your first midterm exam with only a z score written on it. She also told you that a histogram of the scores was approximately normal. How would you interpret each of the following z scores? (a) 2.2 My score was 2.2 standard deviations . of students did better than I did. (b) 0.4 My score was 0.4 standard deviations . I was easily in the of the scores. (c) 1.8 My score was 1.8 standard deviations . I was a little under the percentile on this exam. (d) 1.0 My score was 1 standard deviation . I was around the percentile on this exam. (e) 0 My score was the mean and the median on this exam.
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.
Suppose that your statistics professor returned your first midterm exam with only a z score written on it. She also told you that a histogram of the scores was approximately normal. How would you interpret each of the following z scores?
(a)
2.2
My score was 2.2 standard deviations
.
of students did better than I did.
(b)
0.4
My score was 0.4 standard deviations
. I was easily in the
of the scores.
(c)
1.8
My score was 1.8 standard deviations
. I was a little under the
percentile on this exam.
(d)
1.0
My score was 1 standard deviation
. I was around the
percentile on this exam.
(e)
0
My score was
the mean and
the median on this exam.
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