Draw an example of a data set such that, (a) the data set exhibits central tende

Question

Draw an example of a data set such that, (a) the data set exhibits central tendency. (b) the median of the data set, rather than the mean of the data set, is a better measure of the middle of the data sot. Using Chebyshev's theorem, determine the maximum percentage of data values in a data set that have a z-score with |z| > 3. In recent years, physical anthropologists have been trying to carbon-14 date the remains of ancestors of the famous Homo heidelbergen-sis, found in Baden-Wurttemberg, Germany in 1907. They have determined that the remains are on average 700,000 years old. And the standard deviation of their measurements is 1200 years. (a) Consider one measurement from their data. If the z-score of this measurement is -6, Compute numerical value of the data value. (b) If the z-score of a measurement from this data set is positive, then is that measurement larger than 700,000 years or smaller than 700,000 years? Explain your answer.

Explanation / Answer

Solution:

The central tendency is the extent to which all the data values group around a typical or central value.

The mean is generally used, unless extreme values (outliers) exist.

The median is often used, since the median is not sensitive to extreme values.it is less sensitive to outliers.

Lets take an example of data

11 12 13 14 15

Its mean is (11+12+13+14+15)/5 = 13

So its central tendency is 13. and Its median is also 13

If we take data set 11 12 13 14 15 100

than its mean = (11+12+13+14+15+100)/6 = 27.5

but its median is (13+14)/2 = 13.5

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