If the number of observations in a series is 15, then the third quartile is equal to: 

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SSC CGL Tier-II (JSO) 2022 Official Paper (Held On: 4 March 2023)
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  1. 9th observation in the series after arranging in descending order 
  2. 11th observation in the series after arranging in ascending order 
  3. 10th observation in the series after arranging in descending order 
  4. 12th observation in the series after arranging in ascending order 

Answer (Detailed Solution Below)

Option 4 : 12th observation in the series after arranging in ascending order 
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Detailed Solution

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The correct answer 12th observation in the series after arranging in ascending order. 
Key Points

The method to determine the third quartile of a series with 15 observations is as follows: 

  • First, we need to find the position of the third quartile using the formula:
    • Position of the third quartile = (3/4) * (n + 1); where n represents the total number of observations. In this case, n is 15.
  • Plugging in the values, we have: 
    • Position of the third quartile = (3/4) * (15 + 1) = (3/4) * 16 = 12
    • The position of the third quartile is 12.
  • Next, we arrange the series in ascending order and locate the value at the 12th position. This observation represents the third quartile. (Alternatively, if the series is already sorted in ascending order, the third quartile will be the 12th observation directly.)

Hence, in both cases, the third quartile will be equal to the 12th observation in the series after arranging it in ascending order.

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