# Finish time (minutes) 0 to less than 1(0 10 to less than 20 20 to less than 30 30 to less than 40 40 to less than 50 Numberof athletes 3 10 6 4 2

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.

25 athletes participate in a race and all of them finish it. The distribution of times taken to complete the race by athletes (in minutes) is shown in the table below. Calculate the

This is a problem on finding the mean of continuous grouped data. We first find the midpoint of each interval. For example, the first interval or class is **0 - 10**. The mid-point of this class will be **(0 + 10)/2 = 5.**

We now calculate the product of mid-point and frequency for each class. Here, the number of athletes in each class is the frequency of that class. For example, for the first class **0 – 10**, its frequency is **3**.

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Suppose another researcher takes a random sample of 1000 subjects from the same population (US physicians who received payments from any of 8 major pharmaceutical companies in 2011). You have not yet seen these data. Likely, how will the sample standard deviation of these 1000 values (**s**_{1000}) compare to the sample standard deviation of individual physician payments in the sample of 400 (s_{400}=17 )