Chapter -2 : Practice Questions & Materials

Measure of Variability - Range

1. The monthly electricity consumption for a household varies between 150 kWh and 300 kWh. What is the range of the household's monthly electricity consumption? Solution: Range = Maximum value - Minimum value Range = 300 kWh - 150 kWh = 150 kWh Explanation: To find the range, we subtract the minimum consumption (150 kWh) from the maximum consumption (300 kWh). The range represents the spread of electricity consumption over different months.

2. The monthly income of a freelancer varies from ₹40,000 to ₹80,000. What is the range of the freelancer's monthly income? Solution: Range = Maximum value - Minimum value Range = ₹80,000 - ₹40,000 = ₹40,000 Explanation: The range of the freelancer's income is found by subtracting the minimum income (₹40,000) from the maximum income (₹80,000). This range indicates the income variability each month. 3. Find the range of the monthly rainfall (in mm) for a city over a year: 78, 102, 89, 95, 110, 76, 84, 92, 101, 98, 105, 87. Solution:

Arrange the values in ascending order: 76, 78, 84, 87, 89, 92, 95, 98, 101, 102, 105, 110.

Identify the lowest value (76) and the highest value (110).

Calculate the range: Range = 110 - 76 = 34.

Explanation: To find the range of monthly rainfall, we first ordered the values from lowest to highest. The smallest value is 76 mm, and the highest is 110 mm. Subtracting the smallest value from the highest gives us a range of 34 mm.

4. Find the range of the temperatures (in °C) recorded over a week: 22, 28, 25, 30, 26, 29, 23. Solution:

Arrange the values in ascending order: 22, 23, 25, 26, 28, 29, 30.

Identify the lowest value (22) and the highest value (30).

Calculate the range: Range = 30 - 22 = 8.

Explanation: To find the range of temperatures recorded over a week, we sorted the temperatures from the lowest (22°C) to the highest (30°C). The range is determined by subtracting the lowest temperature from the highest, resulting in a range of 8°C.

5. Find the range of the internet speeds (in Mbps) recorded in different parts of a city: 25, 30, 28, 32, 27, 35, 29, 31, 33, 26. Solution:

Arrange the values in ascending order: 25, 26, 27, 28, 29, 30, 31, 32, 33, 35.

Identify the lowest value (25) and the highest value (35).

Calculate the range: Range = 35 - 25 = 10.

Explanation: To find the range of internet speeds, we sorted the speeds from the lowest (25 Mbps) to the highest (35 Mbps). The range is determined by subtracting the lowest speed from the highest speed, giving a range of 10 Mbps

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