Question

The ages of 25 members of a track and field team are listed below, find the 5-number summary of this data. 19,20,20,21,21,23,23,24,24,24,25,25,26,27,27,29,29,30,31,33,34,35,39,42,48

Answer 1

Answer: 9, 23, 26, 32, 48.

Step-by-step explanation

To find the 5-number summary of this data we have to:

0. Determine the amount of numbers in the data set, which in our case is 25.

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1. Now, we have to organize from smallest to largest: 19, 20, 20, 21, 21, 23, 23, 24, 24, 24, 25, 25, 26, 27, 27, 29, 29, 30, 31, 33, 34, 35, 39, 42, 48.

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2. Next, we have to consider the 1st Quartile equation ¼ (n+1), median equation ½(n+1), and 3rd Quartile ¾(n+1).

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3. Now we have to consider the first number (19) and last number (48), and calculate the 1st, median and 3rd Quartile:

`Q_1=(1)/(4)(25+1)=6.5`
`Q_2=(1)/(2)(25+1)=13`
`Q_3=(3)/(4)(25+1)=19.5`

Therefore, based on the positions, the first quartile is until 23, the median is until 26, and the third is 32.

Finally, the 5-number summary is 19 (minimum), 23 (1st quartile), 26 (median), 32 (3rd quartile), 48 (maximum).