Question

7. What is the interquartile range for the data set?
37, 4, 53, 79, 25, 48, 78, 65, 5, 6, 42, 61.
please show how you the answer.

8. What is the standard deviation for the data set?
112, 149, 112, 148, 139, 121, 116, 134, 148.
Express your answer as a decimal to the nearest tenth.
please show how you got the answer

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.