Monthly Wages

To calculate the first quartile, third quartile, and quartile deviation for the given set of monthly wages (₹), we need to follow a step-by-step process.

Step 1: Sorting the data in ascending order
The given wages in ascending order are:
120, 150, 170, 180, 181, 187, 190, 192, 200, 210

Step 2: Finding the median
The median is the middle value of the data set. Since we have an even number of data points, we find the median by taking the average of the two middle values:
Median = (180 + 181) / 2 = 180.5

Step 3: Finding the first quartile (Q1)
The first quartile is the median of the lower half of the data set. To find Q1, we take the median of the values below the median:
Q1 = (150 + 170) / 2 = 160

Step 4: Finding the third quartile (Q3)
The third quartile is the median of the upper half of the data set. To find Q3, we take the median of the values above the median:
Q3 = (190 + 192) / 2 = 191

Step 5: Calculating the quartile deviation
The quartile deviation is a measure of the spread or dispersion of the data set. It is calculated by taking the difference between Q3 and Q1 and dividing it by 2:
Quartile Deviation = (Q3 - Q1) / 2 = (191 - 160) / 2 = 15.5

Summary:
- The first quartile (Q1) is 160.
- The third quartile (Q3) is 191.
- The quartile deviation is 15.5.

Key Points:
- The first quartile (Q1) is the median of the lower half of the data set.
- The third quartile (Q3) is the median of the upper half of the data set.
- The quartile deviation is calculated as half the difference between Q3 and Q1.