Question

7. What is the interquartile range for the data set?

Answer 1

The given data set is:

37, 4, 53, 79, 25, 48, 78, 65, 5, 6, 42, 61

We arrange the data set in ascending order of magnitude {4,5,6,25,37,42,48,53,61,65,78,79}

The median is 45.

The lower half of the data set is

{4,5,6,25,37,42}

The first quartile is the median of the lower half set;

$Q_1=15.5$

The upper half of the data set is:

{48,53,61,65,78,79}

The median of the upper half is $Q_3=63$.

The inter-quartile range  $Q_3-Q_1=63-15.5=47.5$

8. The given data set is 112, 149, 112, 148, 139, 121, 116, 134, 148.

The mean of the data set is $\bar X =\frac{\sum x}{n}$

$\bar X =\frac{112+149+112+148+139+121+116+134+148}{9}$

$\bar X =\frac{179}{9}=131$

The standard deviation is given by:

$s=\sqrt{\frac{\sum (x-\bar X)^2}{n} }$

$s=\sqrt{\frac{(-19)^2+(18)^2+(-19)^2+(17)^2+(8)^2+(-10)^2+(-15)^2+(3)^2+(18)^2}{9} }$

$s={\frac{\sqrt{2022}}{3}=14.98888477$

The standard deviation is 15.0 to the nearest tenth.