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AMC-8 USA Math Olympiad

Mean and Median calculation AMC 8, 2013 Problem 5

Try this beautiful problem from AMC 8. It involves basic statistics and data representation. We provide sequential hints so that you can try the problem.

What are we learning ?

Competency in Focus: Mean and Median calculation

This problem from American Mathematics Contest 8 (AMC 8, 2013) is based on calculation of mean and median. It is Question no. 5 of the AMC 8 2013 Problem series.

First look at the knowledge graph:-

calculation of  mean and median- AMC 8 2013 Problem

Next understand the problem

Hammie is in the $6^\text{th}$ grade and weighs 106 pounds. His quadruplet sisters are tiny babies and weigh 5, 5, 6, and 8 pounds. Which is greater, the average (mean) weight of these five children or the median weight, and by how many pounds?  
Source of the problem
American Mathematical Contest 2013, AMC 8 Problem 5

Key Competency

Basic Statistics and Data Representation mainly calculation of mean and median.

Difficulty Level
4/10
Suggested Book
Challenges and Thrills in Pre College Mathematics Excursion Of Mathematics 

Start with hints 

Do you really need a hint? Try it first!

Let us first find the median of the weight of the five children. For this, we first have to arrange the weights of the five children in increasing order. As we know, the median is the middle value, if there is an odd number of observations, and if there is an even number of observations, it is the average of the two middle values. Thus, lining up the numbers (5, 5, 6, 8, 106), we see that it  is 6 pounds.

Now what we have to find is the mean of the weights of five children .The average weight of the five kids is $\dfrac{5+5+6+8+106}{5} = \dfrac{130}{5} = 26$.
The median here is obviously less than the mean.
Therefore, the average weight is bigger than median weight , by $26-6 = 20$ pounds, making the answer , average by 20.

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