# STUDENT HEIGHTS

Date of the Problem
August 16, 2021

In June, MATHCOUNTS joined the Data Science 4 Every­one Commitment Campaign to build capacity for K-12 data science ed­ucation. As part of this commitment, MATHCOUNTS will create and share additional resources to help students develop data science skills. The DS4E network, comprised of educators, content developers, policy experts and other advisers, works to raise awareness about data literacy, design curriculum, perform policy advocacy, and create resources for teachers and classrooms.

### Data science is a critically important field, and there are many interesting careers in data science and analytics!

The great news for Mathletes is that the math you do in MATHCOUNTS—such as statistics, problem-solving, pattern recognition and probability—will prepare you to succeed in our data-driven world. Flex those math muscles with this Problem of the Week covering measures of central tendency!  The graphs above show the heights of a class in sixth grade and the heights of that same class in eighth grade. Use the information in the graph to answer the following questions. Note: all heights are given to the nearest inch. What was the range of the class’ heights in 6th grade?

The tallest student in 6th grade was 64 inches, and the shortest was 56 inches. So, the range was 64 – 56 = 8 inches.

What was the positive difference between the median and mean of their sixth grade heights?

The median is the middle height when the heights are placed in order from least to greatest, but since there are an even number of numbers, the median will be the average of the two middle numbers. Thus, the median is (60 + 60)/2 = 60 inches. The mean of the heights is (56 + 57 + 57 + 59 + 59 + 59 + 59 + 59 + 59 + 60 + 60 + 60 + 60 + 60 + 60 + 60 + 60 + 61 + 61 + 61 + 61 + 61 + 62 + 62 + 63 + 64)/26 = 60 inches. So, the difference between the median and the mean is 60 – 60 = 0 inches.

By what percent did the average height increase from sixth grade to eighth grade? Express your answer as a decimal to the nearest tenth.

We established that the average (or mean) of the class in sixth grade was 60 inches. The average of the class in eighth grade was (59 + 60 + 60 + 61 + 61 + 61 + 62 + 62 + 63 + 63 + 63 + 63 + 63 + 64 + 64 + 64 + 64 + 65 + 65 + 65 + 66 + 66 + 66 + 66 + 67 + 68)/26 = 63.5 inches. Thus, the percent increase from sixth to eighth grade was [(63.5 – 60)/60](100) = 5.8%, to the nearest tenth.

Page 1 of the linked PDF contains PROBLEMS & SOLUTIONS.

Page 2 contains ONLY PROBLEMS. ♦

Math topic
CCSS (Common Core State Standard)
Difficulty