To calculate the 10% trimmed mean, for example, the data are ordered low-to-high and the top 10% and the bottom 10% of the data are deleted. The mean of the remaining data is called the “10% trimmed mean.”Please show your work. Compute the mean, the median, the 10% trimmed mean, and the 20% trimmed mean for the DDT concentration in Catfish. For the 10% trimmed mean, delete the ten highest and ten lowest values. For the 20% trimmed mean, delete the 19 highest and lowest values. Order the mean, the median, the 10% trimmed mean, and the 20% trimmed mean from highest to lowest. Discuss why these statistics lie in this order. Add a column to the spreadsheet and compute the base-10 logarithm of the DDT concentrations.
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.
To calculate the 10% trimmed
- Compute the mean, the
median , the 10% trimmed mean, and the 20% trimmed mean for the DDT concentration in Catfish. For the 10% trimmed mean, delete the ten highest and ten lowest values. For the 20% trimmed mean, delete the 19 highest and lowest values. - Order the mean, the median, the 10% trimmed mean, and the 20% trimmed mean from highest to lowest. Discuss why these statistics lie in this order.
- Add a column to the spreadsheet and compute the base-10 logarithm of the DDT concentrations.
- Draw histograms for the DDT concentrations and the logDDT values. For the DDT histogram, use
ranges (“bins”) of 0-5, 5-10, 10-15, … , 70-75. For the logDDT histogram, use ranges of -0.25-0.0, 0.0-0.25, 0.25-0.5, 0.5-0.75, … , 2.25-2.5. Which variable – DDT or logDDT – appears to be morenormally distributed ? - Compute the 95% confidence intervals for DDT concentration and logDDT. The appropriate value of the t-statistic for these confidence intervals is t0.025;95 = 1.985. After you have computed the upper and lower confidence limits for logDDT, convert them into concentration values. Notice how different the confidence intervals are when they are computed on the “raw” data and the log-transformed data. Based on your answer to part (a), which confidence interval do you think makes the most sense?
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