When the frequency distribution is normal

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Q: 142 (IAS/1996)
When the frequency distribution is normal

question_subject: 

Maths

question_exam: 

IAS

stats: 

0,5,9,7,5,2,0

keywords: 

{'frequency distribution': [0, 1, 0, 0], 'median': [0, 1, 0, 0], 'mode': [0, 1, 2, 1], 'mean': [0, 1, 0, 0]}

In a normal frequency distribution, the distribution will appear as a bell curve. In this distribution, the mean, median, and mode are all identical. Let`s dissect all options to understand why option 2 is the correct answer.

Option 1: This option states that the mean, median, and mode are all different from each other. This is incorrect because, in a normal distribution, they are all the same.

Option 2: This is the correct answer. In a normal distribution, the mean (average), median (middle value), and mode (most frequently occurring value) are all identical.

Option 3: This states that the mean is greater than the mode. This can be true in a skewed distribution but not in a normal distribution. In a normal distribution, the mean and mode are equal.

Option 4: Similar to option 3, this might be true in a skewed distribution but not in a normal distribution. In a normal distribution, the mean and median are equal. Hence, the mean cannot be greater than the median.

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