Question

dc stats chp1 & chp2 sections 2.1 - 2.3 fall 2025

1. consider the following data set {0, 1, 9, 7, 3, 5, 5, 6, 4, 32}

a. find the 5 number summary and the mean.
b. what is the range and the iqr?

Explanation:

Step1: Sort the data set

The sorted data set is $\{0,1,3,4,5,5,6,7,9,32\}$.

Step2: Calculate the mean

The mean $\bar{x}=\frac{0 + 1+3+4+5+5+6+7+9+32}{10}=\frac{92}{10}=9.2$.

Step3: Find the 5 - number summary

• Minimum: The smallest value is $0$.
• First - quartile ($Q_1$): The lower half of the data is $\{0,1,3,4,5\}$. The median of this lower half is $3$.
• Median ($Q_2$): Since $n = 10$ (even), the median is the average of the 5th and 6th ordered values. So, $Q_2=\frac{5 + 5}{2}=5$.
• Third - quartile ($Q_3$): The upper half of the data is $\{5,6,7,9,32\}$. The median of this upper half is $7$.
• Maximum: The largest value is $32$.

So the 5 - number summary is $0,3,5,7,32$.

Step4: Calculate the range

The range is the difference between the maximum and minimum values. Range $=32−0 = 32$.

Step5: Calculate the IQR

The inter - quartile range $IQR=Q_3 - Q_1=7 - 3=4$.

Answer:

a. 5 - number summary: $0,3,5,7,32$; Mean: $9.2$
b. Range: $32$; IQR: $4$