We have the dataset:
$53, 46, 50, 48, 39, 43, 41, 40, 39, 40$

Step 1: Arrange the numbers in ascending order.

$39, 39, 40, 40, 41, 43, 46, 48, 50, 53$

Step 2: Find the median (Q2).

The median is the middle number in the dataset. Since there are 10 numbers (an even number of values), the median will be the average of the 5th and 6th numbers.

5th number: 41
6th number: 43
$\text{Median} = \frac{41 + 43}{2} = \frac{84}{2} = 42$

Step 3: Find Q1 (first quartile).

Q1 is the median of the lower half of the dataset (values below the overall median).

Lower half: $39, 39, 40, 40, 41$
Q1 is the middle value of this subset, which is 40.

Step 4: Find Q3 (third quartile).

Q3 is the median of the upper half of the dataset (values above the overall median).

Upper half: $43, 46, 48, 50, 53$
Q3 is the middle value of this subset, which is 48.

Summary:

• Median (Q2) = 42
• Q1 = 40
• Q3 = 48

Would you like more details on any of the steps?

Related Questions:

1. How do you calculate interquartile range (IQR)?
2. What is the significance of quartiles in a data set?
3. How do quartiles relate to box plots?
4. How do you handle outliers using quartiles?
5. Can the median be the same as Q1 or Q3?

Tip: Quartiles are useful for understanding the spread of your data and detecting outliers.