Here is a simple descriptive statistics question.

### Question

When a student Joe, weighing 41 kg, joins a group of students whose average weight is 30 kg, the average weight goes up by 1 kg. Subsequently, if two students, excluding Joe, leave the group the average weight comes back to 30 kg. What is the difference between the average weight of the two students who left and the weight of Joe?

A. 11 kg

B. 5.5 kg

C. 71 kg

D. 36.5 kg

E. 30 kg

### Correct Answer

Choice C. The difference is 5.5 kg.

### Video Explanation

### Explanatory Answer – Method 1

Let the number of students in the group before Joe joined the group be ‘n’.

Description | Number | Average | Sum |
---|---|---|---|

Before Joe | n | 30 | 30n |

Including Joe | (n + 1) | 31 | 31(n + 1) = 31n + 31 |

After 2 leave | (n + 1) – 2 = (n – 1) | 30 | 30(n – 1) = 30n – 30 |

**Step 1**: Compute ‘n’, the number of students before Joe joins.

Sum of weight of n students + weight of Joe = Sum of weight of all (n + 1) students including Joe

30n + 41 = 31(n + 1)

30n + 41 = 31n + 31

Or n = 10.

Number of students before Joe joined = 10.

**Step 2**: Compute sum of weight of the 2 students who leave the group

After Joe joins the group will have 11 students.

When 2 students excluding Joe leave the group, the count will come down to 9 students.

The average weight of the group comes back to 30.

Sum of weights of 11 students = sum of weights of 9 staying in the group + sum of weights of 2 who leave the group.

11 * 31 = 9 * 30 + sum of weights of 2 who leave the group.

341 = 270 + sum of weights of 2 who leave the group

Sum of weights of 2 who leave the group = 341 – 270 = 71.

**Step 3**: Compute average and the difference

Average weight of 2 students who leave = = 35.5

Difference between average weight of 2 students who leave the group and the weight of Joe = 41 – 35.5 = 5.5 kg.

**Choice D is the correct answer**

### Alternative Method

Let the number of students in the group before Joe joins be ‘n’

Joe’s weight is 41 kg. The average weight of n students is 30 kg.

So, Joe weighs 11 kg more than the average weight of n students.

When 2 students excluding Joe leave the group, the average comes back to 30.

The additional 11 kg that Joe added have been nullified when the other 2 students left the group.

2 students took away the extra 11 kg. On average each one took = 5.5 kg.

Joe weighs 11 more than the original average of 30.

The two students who left the group weigh an average of 5.5 kg more than the original average of 30.

So, the required difference = 11 – 5.5 = 5.5 kg.

Oliver Diener says

5.5