There's no 50 in the question but you have used 50 as the maximum instead of 51

Mathematics

ScanSolve AI Answer

Step-by-step solution

2 steps

You are absolutely right! My apologies for that oversight. I incorrectly listed 50 as the maximum value instead of 51 from the original data. Let's correct that.

  1. Rearrange the data and count the number of data points.

    The given data points are: 9, 21, 49, 10, 40, 51, 28, 37, 18, 21, 22, 8, 30, 34, 12, 45, 43, 9, 31, 12.
    Rearranging the data in ascending order:

    8,9,9,10,12,12,18,21,21,22,28,30,31,34,37,40,43,45,49,518, 9, 9, 10, 12, 12, 18, 21, 21, 22, 28, 30, 31, 34, 37, 40, 43, 45, 49, 51

    The number of data points is n=20n = 20.

  2. Calculate the Range.

    The range is the difference between the maximum and minimum values in the dataset.
    Maximum value = 51
    Minimum value = 8

    Range=Maximum value−Minimum value=51−8=43\text{Range} = \text{Maximum value} - \text{Minimum value} = 51 - 8 = \boxed{\text{43}}

    The calculations for Q1, Q3, IQR, and SIQR remain the same as they do not depend on the maximum value being 51 instead of 50 in this specific dataset.

    • Lower Quartile (Q1): 12\boxed{\text{12}}
    • Upper Quartile (Q3): 39.25\boxed{\text{39.25}}
    • Interquartile Range (IQR): 27.25\boxed{\text{27.25}}
    • Semi-Interquartile Range (SIQR): 13.625\boxed{\text{13.625}}
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