The ages of seven policyholders in a portfolio of insurance policies are as follows: 39 34 26 41 70 34 28 (i) Find the median age of the policyholders in this portfolio. (ii) Another policyholder aged 41 years is added to the portfolio. Find the median age of policyholders in the portfolio. (iii) Why would the mean be a poor measure of central tendency for these data? (iv) Calculate the coefficient of variation for this dataset (v) Calculate the z-scores for the dataset and identify any outliers present (vi) Construct a boxplot and explain the shape of the distribution for this dataset
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 ages of seven policyholders in a portfolio of insurance policies are as follows:
39 34 26 41 70 34 28
(i) Find the median age of the policyholders in this portfolio.
(ii) Another policyholder aged 41 years is added to the portfolio. Find the median age
of policyholders in the portfolio.
(iii) Why would the mean be a poor measure of
(iv) Calculate the coefficient of variation for this dataset
(v) Calculate the z-scores for the dataset and identify any outliers present
(vi) Construct a boxplot and explain the shape of the distribution for this dataset
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