Question

a math teacher recorded the number of minutes 9 students spent studying for their math test over the weekend. data (in minutes): 25, 40, 30, 60, 35, 55, 20, 50, 45. use this information to calculate the median, mean, q1, q3, and iqr. median: mean: q1:

Explanation:

Step1: Sort the data

$20, 25, 30, 35, 40, 45, 50, 55, 60$

Step2: Calculate the median

There are 9 data - points. The median is the 5th value. So, median = $40$.

Step3: Calculate the mean

The mean $\bar{x}=\frac{20 + 25+30 + 35+40+45+50+55+60}{9}=\frac{360}{9}=40$.

Step4: Calculate Q1

The lower half of the data is $20, 25, 30, 35$. The median of the lower half (Q1) is $\frac{25 + 30}{2}=27.5$.

Step5: Calculate Q3

The upper half of the data is $45, 50, 55, 60$. The median of the upper half (Q3) is $\frac{50+55}{2}=52.5$.

Step6: Calculate the IQR

The inter - quartile range IQR = Q3 - Q1. So, IQR=$52.5−27.5 = 25$.

Answer:

Median: $40$
Mean: $40$
Q1: $27.5$
Q3: $52.5$
IQR: $25$