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Find the median, the lower half and the upper half of the history 108 test scores...

Find the median, the lower half and the upper half of the history 108 test scores 10,16,14,22,21,13,15,14,10,18,19,8,16,12,18,11,9,10,15,10,21,14,18,19,1819,3,25,18,13,1,16,9,14,821,13,14,18,16,5,11,17,14,12,16,18,16,18,17,10,12,19,9,3,15,17

Solutions

Expert Solution

The median is the middle number in a sorted list of numbers. So, to find the median, we need to place the numbers in value order and find the middle number.

Ordering the data from least to greatest, we get:

1   3   3   5   8   9   9   9   10   10   10   10   10   11   11   12   12   12   13   13   13   14   14   14   14   14   14   15   15   15   16   16   16   16   16   16   17   17   17   18   18   18   18   18   18   18   19   19   19   21   21   22   25   821   1819   

So, the median is 15 .

The first quartile (or lower quartile or 25th percentile) is the median of the bottom half of the numbers. So, to find the first quartile, we need to place the numbers in value order and find the bottom half.

1   3   3   5   8   9   9   9   10   10   10   10   10   11   11   12   12   12   13   13   13   14   14   14   14   14   14   15   15   15   16   16   16   16   16   16   17   17   17   18   18   18   18   18   18   18   19   19   19   21   21   22   25   821   1819   

So, the bottom half is

1   3   3   5   8   9   9   9   10   10   10   10   10   11   11   12   12   12   13   13   13   14   14   14   14   14   14   

The median of these numbers is 11.

The third quartile (or upper quartile or 75th percentile) is the median of the upper half of the numbers. So, to find the third quartile, we need to place the numbers in value order and find the upper half.

1   3   3   5   8   9   9   9   10   10   10   10   10   11   11   12   12   12   13   13   13   14   14   14   14   14   14   15   15   15   16   16   16   16   16   16   17   17   17   18   18   18   18   18   18   18   19   19   19   21   21   22   25   821   1819   

So, the upper half is

15   15   16   16   16   16   16   16   17   17   17   18   18   18   18   18   18   18   19   19   19   21   21   22   25   821   1819   

The median of these numbers is 18.

milcah answered 5 months ago
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