Question

question #8
which data set best represents normally distributed data?
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Explanation:

Step1: Recall normal distribution properties

A normal distribution is symmetric about the mean. The frequencies should increase to a peak (around the mean) and then decrease symmetrically.

Step2: Analyze the first data - set

For the first data - set:

• The frequencies are \(5,20,4,21,5\).
• If we consider the middle class (say \(32 - 38\) as a central candidate), the frequencies on either side (\(25 - 31\) and \(39 - 45\)) are \(20\) and \(21\) (relatively close), and the outer - class frequencies (\(18 - 24\) and \(46 - 52\)) are \(5\) each. This shows a symmetric pattern.

Step3: Analyze the second data - set

For the second data - set:

• The frequencies are \(1,4,8,18,36\).
• The frequencies are increasing but not symmetric around a central point.

Step4: Analyze the third data - set

For the third data - set:

• The frequencies are \(20,9,2,10,19\).
• There is no clear symmetry. The left - most class (\(18 - 24\)) has a high frequency (\(20\)) and the distribution is not symmetric.

Step5: Analyze the fourth data - set

For the fourth data - set:

• The frequencies are \(1,11,38,10,2\).
• The left - most class (\(18 - 24\)) has a very low frequency (\(1\)) and the right - most class (\(46 - 52\)) has a very low frequency (\(2\)), but the distribution is not symmetric around the central class (\(32 - 38\)).

Answer:

The first data - set (with frequencies \(5,20,4,21,5\)) best represents normally distributed data.