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The first 11 prime numbers are as follow:

2,3,5,7,11,13,17,19,23,29,31
what are the first and third quartiles?

1 answer

To find the first and third quartiles of the given data set of the first 11 prime numbers (2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31), we can follow these steps:

  1. Order the data: The data is already ordered.

  2. Calculate the median (Q2):

    • Since there are 11 numbers (odd), the median is the middle number, which is the 6th number in the ordered list.
    • The 6th number is 13.

  3. Calculate the first quartile (Q1):

    • Q1 is the median of the first half of the data (not including the overall median if the count is odd).
    • The first half consists of the first five numbers: 2, 3, 5, 7, 11.
    • The median of this subset (Q1) is the 3rd number, which is 5.

  4. Calculate the third quartile (Q3):

    • Q3 is the median of the second half of the data (not including the overall median).
    • The second half consists of the numbers after the median: 13, 17, 19, 23, 29, 31.
    • The median of this subset (Q3) is the 3rd number, which is 23.

So, the first quartile (Q1) is 5, and the third quartile (Q3) is 23.