Calculate the interquartile range (IQR) and semi-interquartile range (SIQR) for the following height data…

Question

Calculate the interquartile range (IQR) and semi-interquartile range (SIQR) for the following height data: 17, 16, 19, 18, 17, 18, 17, 19, 16, 19.

ScanSolve AI Tutor · Accepted Answer

To solve question 10, we need to find the interquartile range (IQR) and the semi-interquartile range (SIQR) of the given height distribution.

The height data is: 17, 16, 19, 18, 17, 18, 17, 19, 16, 19.
There are $n=10$ data points.

Order the data from least to greatest.
$16, 16, 17, 17, 17, 18, 18, 19, 19, 19$
Calculate the first quartile ( $Q_1$ ).
$Q_1$ is the median of the lower half of the data. Since $n=10$ is an even number, the lower half consists of the first $n/2 = 5$ values.
Lower half: 16, 16, 17, 17, 17
The median of these 5 values is the middle value, which is 17.
So, $Q_1 = 17$ inches.
Calculate the third quartile ( $Q_3$ ).
$Q_3$ is the median of the upper half of the data. The upper half consists of the last $n/2 = 5$ values.
Upper half: 18, 18, 19, 19, 19
The median of these 5 values is the middle value, which is 19.
So, $Q_3 = 19$ inches.
Calculate the Interquartile Range (IQR).
The IQR is the difference between the third quartile and the first quartile.
$\text{IQR} = Q_3 - Q_1$ $\text{IQR} = 19 - 17 = 2 \text{ inches}$
Calculate the Semi-Interquartile Range (SIQR).
The SIQR is half of the interquartile range.
$\text{SIQR} = \frac{\text{IQR}}{2}$ $\text{SIQR} = \frac{2}{2} = 1 \text{ inch}$
The interquartile range is 2 inches and the semi-interquartile range is 1 inch.

The final answer is $\boxed{\text{Interquartile Range: 2 inches, Semi-Interquartile Range: 1 inch}}$ .

Calculate the interquartile range (IQR) and semi-interquartile range (SIQR) for the following height data: 17, 16, 19, 18, 17, 18, 17, 19, 16, 19.