Data 27,17,26,23,28,19,20,24.what is the range, first quartile, third quartile, and quartile deviation?

To find the range, first quartile, third quartile, and quartile deviation, we first need to arrange the data in ascending order:

17, 19, 20, 23, 24, 26, 27, 28

Range = Maximum value - Minimum value
Range = 28 - 17
Range = 11

To find the first quartile (Q1), we need to find the median of the lower half of the data set:

Lower half: 17, 19, 20, 23
Q1 = (19 + 20) / 2
Q1 = 19.5

To find the third quartile (Q3), we need to find the median of the upper half of the data set:

Upper half: 24, 26, 27, 28
Q3 = (26 + 27) / 2
Q3 = 26.5

Quartile deviation = (Q3 - Q1) / 2
Quartile deviation = (26.5 - 19.5) / 2
Quartile deviation = 7 / 2
Quartile deviation = 3.5

Therefore, the range is 11, the first quartile is 19.5, the third quartile is 26.5, and the quartile deviation is 3.5.

1. Range = 11
Range is the difference between the largest and smallest values in a dataset. In this case, the largest value is 28 and the smallest value is 17, so the range is 28 - 17 = 11.

2. First quartile (Q1) = 19
First quartile is the median of the lower half of the dataset. To find Q1, we first sort the data in ascending order: 17, 19, 20, 23, 24, 26, 27, 28. The median of the lower half is 19, so Q1 is 19.

3. Third quartile (Q3) = 26
Third quartile is the median of the upper half of the dataset. To find Q3, we consider the data from Q1 onwards: 19, 20, 23, 24, 26, 27, 28. The median of this half is 26, so Q3 is 26.

4. Quartile deviation (QD) = 3.5
Quartile deviation is half of the difference between Q3 and Q1. In this case, QD = (26 - 19) / 2 = 3.5.