Question

1. data set: 5, 2, 8, 4, 7, 10, 13, 12, put data in order: ____________ median = _ upper quartile= _ lower quartile = _ iqr = ____________

Explanation:

Step1: Sort the data set

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

Step2: Find the median

Since there are 8 data - points, the median is the average of the 4th and 5th ordered values. $\text{Median}=\frac{7 + 8}{2}=7.5$

Step3: Find the lower half and upper half of the data

The lower half is $2,4,5,7$ and the upper half is $8,10,12,13$

Step4: Find the lower quartile

The lower quartile ($Q_1$) is the median of the lower half. Since there are 4 values in the lower half, $Q_1=\frac{4 + 5}{2}=4.5$

Step5: Find the upper quartile

The upper quartile ($Q_3$) is the median of the upper half. Since there are 4 values in the upper half, $Q_3=\frac{10+12}{2} = 11$

Step6: Calculate the inter - quartile range (IQR)

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

Answer:

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