Question

interquartile range- practice worksheet 1
{6,12,8,15,9,7}
median 8.5
q3 12
q1 7
iqr 5
{5,9,17,25,36,45}
median 21
q3 36
q1 9
iqr 27
{3,14,28,22,5,9}
median 11.5
q3 22
q1 5
iqr 17
{8,11,32,29,9,34}
median 10
q3 29
q1 9
iqr 21
{2,12,52,33,8,14}
median
q3
q1
iqr
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Explanation:

Step1: Arrange data in ascending order

For the set $\{2,12,52,33,8,14\}$, the ordered - set is $\{2,8,12,14,33,52\}$.

Step2: Find the median

Since there are $n = 6$ data points, the median is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+1)$th ordered values. $\frac{6}{2}=3$ and $\frac{6}{2}+1 = 4$. The median is $\frac{12 + 14}{2}=13$.

Step3: Find Q1

The lower half of the data is $\{2,8,12\}$. Since there are $n_1=3$ data points in the lower half, the first - quartile $Q1$ is the middle value of the lower half, so $Q1 = 8$.

Step4: Find Q3

The upper half of the data is $\{14,33,52\}$. Since there are $n_2 = 3$ data points in the upper half, the third - quartile $Q3$ is the middle value of the upper half, so $Q3=33$.

Step5: Calculate IQR

The inter - quartile range $IQR=Q3 - Q1$. So $IQR=33 - 8=25$.

Answer:

Median: 13
Q1: 8
Q3: 33
IQR: 25