Question

1. data set: 5, 2, 8, 4, 7, 10, 13, 12. put data in order: __ median = upper quartile = lower quartile = iqr = 2) data set: 23, 18, 17, 9, 21, 27, 12, 14, 13, 16. put data in order: median = upper quartile = lower quartile = iqr = 3) data set: 5, 10, 3, 6, 8, 12, 18, 23, 26, 12, 23. put data in order: median = upper quartile = lower quartile = iqr = __

Explanation:

1. First data - set: 5, 2, 8, 4, 7, 10, 13, 12

Step1: Order the data

$2,4,5,7,8,10,12,13$

Step2: Find the median

Since there are $n = 8$ data - points, the median is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+1)$th ordered values. $\frac{n}{2}=4$ and $\frac{n}{2}+1 = 5$. The median $M=\frac{7 + 8}{2}=7.5$

Step3: Find the lower quartile

The lower half of the data is $2,4,5,7$. Since there are $n_1=4$ data - points in the lower half, the lower quartile $Q_1$ is the average of the $\frac{n_1}{2}$th and $(\frac{n_1}{2}+1)$th ordered values. $\frac{n_1}{2}=2$ and $\frac{n_1}{2}+1 = 3$. So $Q_1=\frac{4 + 5}{2}=4.5$

Step4: Find the upper quartile

The upper half of the data is $8,10,12,13$. Since there are $n_2 = 4$ data - points in the upper half, the upper quartile $Q_3$ is the average of the $\frac{n_2}{2}$th and $(\frac{n_2}{2}+1)$th ordered values. $\frac{n_2}{2}=2$ and $\frac{n_2}{2}+1 = 3$. So $Q_3=\frac{10+12}{2}=11$

Step5: Calculate the IQR

$IQR=Q_3 - Q_1=11 - 4.5 = 6.5$

Step1: Order the data

$9,11,12,13,16,17,18,21,23,27$

Step2: Find the median

Since there are $n = 10$ data - points, the median is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+1)$th ordered values. $\frac{n}{2}=5$ and $\frac{n}{2}+1 = 6$. The median $M=\frac{16 + 17}{2}=16.5$

Step3: Find the lower quartile

The lower half of the data is $9,11,12,13,16$. Since there are $n_1 = 5$ data - points in the lower half, the lower quartile $Q_1$ is the third - ordered value. So $Q_1 = 12$

Step4: Find the upper quartile

The upper half of the data is $17,18,21,23,27$. Since there are $n_2 = 5$ data - points in the upper half, the upper quartile $Q_3$ is the third - ordered value. So $Q_3=21$

Step5: Calculate the IQR

$IQR=Q_3 - Q_1=21 - 12 = 9$

Step1: Order the data

$3,5,6,8,10,12,12,18,23,23,26$

Step2: Find the median

Since there are $n = 11$ data - points, the median is the $\frac{n + 1}{2}$th ordered value. $\frac{n+1}{2}=6$. The median $M = 12$

Step3: Find the lower quartile

The lower half of the data is $3,5,6,8,10$. Since there are $n_1 = 5$ data - points in the lower half, the lower quartile $Q_1$ is the third - ordered value. So $Q_1 = 6$

Step4: Find the upper quartile

The upper half of the data is $12,18,23,23,26$. Since there are $n_2 = 5$ data - points in the upper half, the upper quartile $Q_3$ is the third - ordered value. So $Q_3=23$

Step5: Calculate the IQR

$IQR=Q_3 - Q_1=23 - 6 = 17$

Answer:

Put Data in Order: $2,4,5,7,8,10,12,13$
Median $=7.5$
Upper Quartile $=11$
Lower Quartile $=4.5$
IQR $=6.5$

2. Second data - set: 23, 18, 17, 9, 21, 27, 12, 11, 13, 16