Consider a data set with at least three data values. Suppose the highest value is increased by 10 and the lowest is decreased by 10. (a) Does the mean change? Explain. No, the sum of the data does not change. O No, the number of data values does not change. O Yes, changing the extreme data values affects the mean. O Yes, the sum of the data changes. O Yes, the number of data values changes. (b) Does the median change? Explain. O No, changing the extreme data values does not affect the median. O No, the sum of the data does not change. O Yes, the number of data values changes. O No, the number of data values does not change. O Yes, the sum of the data changes. (c) Is it possible for the mode to change? Explain. O No, all values will still occur at the same frequency. O Yes, depending on the number a data values. O Yes, depending on which data value occurs most frequently after the data are changed. O No, the only change is an increased frequency of 1 for the extreme values. O Yes, depending on the range of the data values.
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.
In statistics , Mean, median and mode are all measures of central tendency .
Mean :
It is the same as the average value of a data set and is found using a calculation. Add up all of the numbers and divide by the number of numbers in the data set.
Median :
It is the central number of a data set. Arrange data points from smallest to largest and locate the central number. This is the median. If there are 2 numbers in the middle, the median is the average of those 2 numbers.
Mode :
It is the number in a data set that occurs most frequently. Count how many times each number occurs in the data set. The mode is the number with the highest tally. It's ok if there is more than one mode. And if all numbers occur the same number of times there is no mode.
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