Question

the list below shows the ages (in years) of 10 people riding in a van to a math competition. calculate the mean age of the people in the van. round your answer to the nearest tenth of a year.
ages 11 10 15 11 14 13 14 14 15 31
mean = years (please round your answer to the nearest tenth.)
median = years (please enter an exact answer.)
hint: textbook measures of center

Explanation:

Mean Calculation

Step1: Sum all ages

We add up all the given ages: \(11 + 10 + 15 + 11 + 14 + 13 + 14 + 14 + 15 + 31\). Let's calculate that: \(11+10 = 21\), \(21+15 = 36\), \(36+11 = 47\), \(47+14 = 61\), \(61+13 = 74\), \(74+14 = 88\), \(88+14 = 102\), \(102+15 = 117\), \(117+31 = 148\). So the sum of ages is \(148\).

Step2: Divide by number of people

There are 10 people, so the mean is \(\frac{148}{10}=14.8\) (already to the nearest tenth as it's a one - decimal place number after division).

Median Calculation

Step1: Order the ages

First, we order the ages from least to greatest: \(10, 11, 11, 13, 14, 14, 14, 15, 15, 31\).

Step2: Find the middle value(s)

Since there are 10 values (an even number), the median is the average of the 5th and 6th values. The 5th value is \(14\) and the 6th value is also \(14\). So the median is \(\frac{14 + 14}{2}=14\).

Answer:

Mean = \(14.8\) years
Median = \(14\) years