Sand and clay studies were conducted at a site in California. Twelve consecutive depths, each about 15 cm deep, were studied and the following percentages of sand in the soil were recorded. 22.8 30.1 26.4 20.5 23.5 22.2 23.7 28.4 28.1 29.0 28.6 24.0 Convert this sequence of numbers to a sequence of symbols A and B, where A indicates a value above the median and B denotes a value below the median.
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.
Sand and clay studies were conducted at a site in California. Twelve consecutive depths, each about 15 cm deep, were studied and the following percentages of sand in the soil were recorded.
|
22.8 |
30.1 |
26.4 |
20.5 |
23.5 |
22.2 |
|
23.7 |
28.4 |
28.1 |
29.0 |
28.6 |
24.0 |
Convert this sequence of numbers to a sequence of symbols A and B, where A indicates a value above the median and B denotes a value below the median.
The twelve consecutive depth are: 22.8, 30.1, 26.4, 20.5, 23.5, 22.2, 23.7, 28.4, 28.1, 29.0, 28.6, 24.0
To convert the above sequence of numbers to a sequence of symbols A and B, the median is required.
To find the median of the above numbers, arrange them in ascending (increasing) order.
Ascending order: 20.5, 22.2, 22.8, 23.5, 23.7, 24.0, 26.4, 28.1, 28.4, 28.6, 29.0, 30.1
Since the number of observations (n) is equal12 (even number) the formula for median will be :
Note: The observations need to be selected from ascending order.
Here, n=12 therefore,
Here, 6th observation is 24.0 and 7th observation is 26.4. in the ascending order.
Therefore the median will be:
The value of the median is 25.2 for the above sequence.
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