Let's solve the problem step by step.

Given data:

The daily wages (in rupees) of 19 workers:
41, 21, 38, 27, 31, 45, 23, 26, 29, 30, 28, 25, 35, 42, 47, 53, 29, 31, 35

Step 1: Arrange the data in ascending order

23, 25, 26, 27, 28, 29, 29, 30, 31, 31, 31, 35, 35, 38, 41, 42, 45, 47, 53

Step 2: Find the median

• The median is the middle value. Since there are 19 numbers, the median is the 10th value in the ordered set.
• The 10th value is 31.
• Median = 31

Step 3: Find the lower quartile (Q1)

• The lower quartile (Q1) is the median of the first half (excluding the median itself).
• The first 9 values: 23, 25, 26, 27, 28, 29, 29, 30, 31
• The median of these 9 values is the 5th value, which is 28.
• Lower quartile (Q1) = 28

Step 4: Find the upper quartile (Q3)

• The upper quartile (Q3) is the median of the second half (excluding the median itself).
• The last 9 values: 31, 35, 35, 38, 41, 42, 45, 47, 53
• The median of these 9 values is the 5th value, which is 41.
• Upper quartile (Q3) = 41

Step 5: Find the interquartile range (IQR)

• IQR = Q3 - Q1 = 41 - 28 = 13

Final Answers:

1. Median = 31
2. Lower quartile (Q1) = 28
3. Upper quartile (Q3) = 41
4. Interquartile range (IQR) = 13

Would you like a detailed explanation of any step?

Related Questions:

1. How do you find the median in an even set of numbers?
2. What is the significance of the interquartile range?
3. How can quartiles be used to detect outliers?
4. How do you interpret the spread of data using quartiles?
5. What other methods can be used to measure data dispersion?

Tip:

The interquartile range (IQR) is useful for identifying outliers. Any value 1.5 times the IQR above Q3 or below Q1 is considered an outlier!