Statistics Test - 12

It is given that the mean weight of 6 students and a teacher is 41 kg.

∴ Sum of the weights of 7 persons = 41 kg × 7 = 287 kg ... (1)

It is given that if the weight of the teacher is excluded, then the mean weight gets reduced by 2.5 kg.

∴ Mean weight of 6 students = 41 kg − 2.5 kg = 38.5 kg

∴ Sum of the weights of 6 students = 6 × 38.5 kg = 231 kg ... (2)

From (1) and (2):

Weight of the teacher = 287 kg − 231 kg = 56 kg

Thus, the weight of the teacher is 56 kg.

The correct answer is C.

For the data of the weights of 10 persons, the median weight is the mean of the 5^th and 6^th observations when the weights are arranged in either increasing or decreasing order.

Let the data be arranged in increasing order. In this case, the maximum value of the 5^th observation can be 61 kg.

When one more person joins the group, the new median weight (68 kg) will be the 6^th observation. Clearly, the 6^th observation in this case will be 68 kg. Now, as the median weight has increased, the weight of the new person has to be more than 61 kg.

If the new person’s weight lies between 61 kg and 68 kg, the new median weight will be same as the weight of that person. We are given that the new median weight is 68 kg. Hence, the weight of the new person will be 68 kg or more.

Hence, the minimum weight of the new person is 68 kg.

The correct answer is C.