Mathematics Class 10: Median and Mode

Study Notes

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%.

Description

In this exercise, you'll find the values of x and the mode from a set of 10 observations arranged in ascending order. You will apply your understanding of median calculations with even sets of data and practice determining the mode. This activity reinforces concepts of central tendency in statistics.