The weight of 12 students(in kg) are:40, 61, 54, 50, 59, 37, 51, 41, 48, 62, 46 and 34.(i) Calculate the mean weight and the median weight.(ii) After 6 months the weight of each student increases by 4 kg, find thenew mean weight.(iii) If the weight of one students was misread as 34 instead of 28, findthe correct median weight.

(i) To calculate the mean weight, you add up all the weights and divide by the number of students.

40 + 61 + 54 + 50 + 59 + 37 + 51 + 41 + 48 + 62 + 46 + 34 = 583 kg

Then divide by the number of students, which is 12.

583 / 12 = 48.58 kg (rounded to two decimal places)

The median weight is the middle value when the weights are arranged in ascending order. If there is an even number of values, the median is the average of the two middle values.

First, arrange the weights in ascending order: 34, 37, 40, 41, 46, 48, 50, 51, 54, 59, 61, 62

The two middle values are 48 and 50. The median is the average of these two values.

(48 + 50) / 2 = 49 kg

(ii) If the weight of each student increases by 4 kg, the total weight increases by 4 kg times the number of students.

4 kg * 12 students = 48 kg

Add this to the original total weight and divide by the number of students to find the new mean weight.

(583 kg + 48 kg) / 12 students = 52.58 kg (rounded to two decimal places)

(iii) If one student's weight was misread as 34 kg instead of 28 kg, you need to subtract the difference from the total weight and recalculate the median.

The difference is 34 kg - 28 kg = 6 kg

Subtract this from the original total weight: 583 kg - 6 kg = 577 kg

Then arrange the corrected weights in ascending order: 28, 37, 40, 41, 46, 48, 50, 51, 54, 59, 61, 62

The two middle values are still 48 and 50, so the median remains 49 kg.