The arithmetic mean of the following frequency distribution of number of accidents X on week working days is:

X: 2 4 6 8 10 12
Frequency: 3 4 2 1 4 2

 

This question was previously asked in
SSC CGL Tier-II ( JSO ) 2021 Official Paper ( Held On: 10 August 2022 )
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  1. 4.625
  2. 6.625
  3. 7.625
  4. 5.625

Answer (Detailed Solution Below)

Option 2 : 6.625
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PYST 1: SSC CGL - English (Held On : 11 April 2022 Shift 1)
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Detailed Solution

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The correct answer is 6.625

 Key Points

  • Arithmetic mean is a commonly used measure of central tendency that gives an average of a set of numbers.
  • The formula for finding the arithmetic mean is: \((sum of data points x frequency) / total frequency.\)
  • The arithmetic mean can be sensitive to extreme values  in the data set.
  • There are other measures of central tendency, such as the median and mode, that can provide a better representation of the data in some cases.

Additional Information 

  • To find the arithmetic mean (also known as the average), we first need to find the sum of the products of each data point and its frequency, and then divide by the total frequency.
  • This can be done as follows:
    • \((2 x 3) + (4 x 4) + (6 x 2) + (8 x 1) + (10 x 4) + (12 x 2) = 6 + 16 + 12 + 8 + 40 + 24 = 106\)
  • Total frequency = \(3 + 4 + 2 + 1 + 4 + 2 = 16\)
  • Arithmetic mean = \(106 / 16 = 6.625\)
  • Understanding the concept of central tendency and the various measures used to describe it is important for data analysis and interpretation.
  • It is important to choose the appropriate measure of central tendency depending on the type and distribution of the data being analyzed.

 

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