The following histogram shows the temperature measured at 12 noon on every day of a fifteen-year period for the U.S. city of Philadelphia (5,471 days) with: Mean: 54; Median 55; SD 18 A. How would you characterize this distribution (symmetric, right skewed, or left skewed) without calculations? Justify the answer properly. B. Whether the data is unimodal or bi-modal. Give proper reasoning. C. What formula for the median calculation has been used in this problem? D. Is it possible to compute the variance of the data,
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.
Q1. The following histogram shows the temperature measured at 12 noon on every day of a fifteen-year period for the U.S. city of Philadelphia (5,471 days) with:
Mean: 54;
SD 18
A. How would you characterize this distribution (symmetric, right skewed, or left skewed) without calculations? Justify the answer properly.
B. Whether the data is unimodal or bi-modal. Give proper reasoning.
C. What formula for the median calculation has been used in this problem?
D. Is it possible to compute the variance of the data, if it is so, what will be the variance of the data?
E. What is the kurtosis measure?
F. Consider a small sample of temperatures (12, 13 54 56 25). For this sample calculate the type of kurtosis present. Make proper graphs.
**answer the last 3 parts
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