Histograms of random sample data are often used as an indication of the shape of the underlying population distribution. The histograms on below are based on random samples of size 30, 50, and 100 from the same population.
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.
Histograms of random sample data are often used as an indication of the shape of the underlying population distribution. The histograms on below are based on random samples of size 30, 50, and 100 from the same population.
(a) Using the midpoint labels of the three histograms, what would you say about the estimated
Complete the table giving the range of the sample data in each of the histograms.
| Smallest Value | Largest Value | |
| Histogram (i) | ||
| Histogram (ii) | ||
| Histogram (iii) |
Based on the completed table, select the most reasonable estimate of the range of the population data.
(a) From the picture given:
| Smallest Value | Largest Value | |
| Histogram (i) | 9.5 | 14 |
| Histogram (ii) | 9 | 14 |
| Histogram (iii) | 9.5 | 14.5 |
Based on the table, the most reasonable estimate of the range of the population data is option (iv) 9 to 15.
Option (i) Since there are very few values outside the range 10 to 14, we can say that the bulk of the data is between 10 and 14.
This is the correct option for this.
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