Question

consider the two data sets below:
data set 1: 19, 25, 35, 38, 41, 49, 50, 52, 59
data set 2: 19, 25, 35, 38, 41, 49, 50, 52, 99

which of the following statements is true?

the values are not in order.
the data sets will have different values for their interquartile range.
the data sets will have the same values for their interquartile range.
an outlier will have no effect on the range.

Explanation:

Step1: Verify data order

Both data sets are sorted ascendingly, so first option is false.

Step2: Calculate IQR for Data Set1

Data Set1: $19, 25, 35, 38, 41, 49, 50, 52, 59$

• Median (Q2) = 41
• Lower half: $19,25,35,38$; Q1 = $\frac{25+35}{2}=30$
• Upper half: $49,50,52,59$; Q3 = $\frac{50+52}{2}=51$
• IQR = $51-30=21$

Step3: Calculate IQR for Data Set2

Data Set2: $19, 25, 35, 38, 41, 49, 50, 52, 99$

• Median (Q2) = 41
• Lower half: $19,25,35,38$; Q1 = $\frac{25+35}{2}=30$
• Upper half: $49,50,52,99$; Q3 = $\frac{50+52}{2}=51$
• IQR = $51-30=21$

Step4: Evaluate range claim

Range of Data Set1: $59-19=40$; Range of Data Set2: $99-19=80$. Outlier changes range, so last option is false.

Answer:

The data sets will have the same values for their interquartile range.