Mathematics Class 10: Median and Mode

Observations and Median Calculation

• 10 observations in ascending order: 45, 47, 50, 52, x, x + 2, 60, 62, 63, 74.
• Median calculated as the average of the 5th and 6th values: x and x + 2.
• Given median value is 53; set up equation: (x + (x + 2)) / 2 = 53.
• Simplifying gives: 2 x + 2 = 106; thus, 2 x = 104 and x = 52.
• Updated observation list after finding x: 45, 47, 50, 52, 52, 54, 60, 62, 63, 74.
• Mode defined as the most frequently occurring number; here, mode = 52 since it appears twice.

Profit Calculation for Investments

• Mr. Sayyad's investment: Rs. 40,000 at 8% compound interest over 2 years.
• Calculation of the amount (A) using the formula: A = P (1 + R/100)^N.
• Substituting values gives: A = 40,000 * (1.08)^2 = 46,656 Rs.
• Compound interest (I) computed as: I = A - P = 46,656 - 40,000 = 6,656 Rs.
• Percentage profit for Mr. Sayyad calculated as: (6,656 / 40,000) * 100 = 16.64%.

Mr. Fernandes' Investment Details

• Mr. Fernandes invested Rs. 1,20,000 in a mutual fund for 2 years.
• Amount received after 2 years: Rs. 1,92,000.
• Gain from investment calculated as: 1,92,000 - 1,20,000 = 72,000 Rs.
• Percentage of profit is derived from: (72,000 / 1,20,000) * 100 = 60.00%.