The following stem-and-leaf plot represents the test scores for 2626 students in a class on their most recent test. Use the data provided to find the quartiles. Find the second quartile.
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.
The following stem-and-leaf plot represents the test scores for 2626 students in a class on their most recent test. Use the data provided to find the quartiles.
Find the second quartile.
Stem |Leaves
6 |0 1 2 2 4 7 8
7 |0 1 2 5 8
8 |3 6 6 7 9 9
9 |0 1 2 2 2 4 5 8
Stemplot:
Stemplot is a graphical representation for a given numerical data and it is used to find the shape of a distribution.
Steps for obtaining original data from Stemplot:
- In stem plot each of the observation is separated into two parts, the leading digit is the stem and the remaining digit is the leaf.
- All the stem values are shown vertically in one column towards left side of vertical line.
- The leaf values are placed for each of the corresponding stem to the right of the vertical line. The leaf values also starts with a smaller value.
- To obtain the original data set combine value of stem with corresponding values in the leaf.
In the given Stemplot the stem values are 6, 7, 8, and 9. The leaf values corresponding to 6 is 0, 1, 2, 2, 4, 7, 8, the leaf values corresponding to 7 is 0, 1, 2, 5, 8, the leaf values corresponding to 8 is 3, 6, 6, 7, 9, 9, and the leaf values corresponding to 9 is 0, 1, 2, 2, 2, 4, 5, 8.
The original data set from the Stemplot is 60, 61, 62, 62, 64, 67, 68, 70, 71, 72, 75, 78, 83, 86, 86, 87, 89, 89, 90, 91, 92, 92, 92, 94, 95, and 98.
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