Question

3 - 115. louis recorded how many times he could jump rope without stopping. here is his data: 50 15 102 64 29 55 100 97 48 81 61 find the median, upper quartile, and lower quartile of his data. 3 - 116. find the area and perimeter of the shape below. show your work. 3 - 117. this problem is a checkpoint for unit rates and proportions. it will be referred to as checkpoint 3. in parts (a) through (c), use the given information to find the unit rate. in parts (d) through (f), write and solve a proportion based on the given information. a. if $2\frac{1}{4}$ pounds of bananas cost $1.89, what is the cost per pound? b. what is the weight per cm?

Explanation:

Step1: Sort the data

Sort the data set \(50,15,102,64,29,55,100,97,48,81,61\) in ascending order: \(15,29,48,50,55,61,64,81,97,100,102\)

Step2: Find the median

The median is the middle value of a sorted data set. Since there are \(n = 11\) data points, the median is the \(\frac{n + 1}{2}\) -th value. \(\frac{11+ 1}{2}=6\) -th value. So the median is \(61\)

Step3: Find the lower quartile

The lower quartile \(Q_1\) is the median of the lower half of the data. The lower half of the data is \(15,29,48,50,55\). Since there are \(n = 5\) data points in the lower half, the lower quartile is the \(\frac{5 + 1}{2}=3\) -th value. So \(Q_1 = 48\)

Step4: Find the upper quartile

The upper quartile \(Q_3\) is the median of the upper half of the data. The upper half of the data is \(64,81,97,100,102\). Since there are \(n = 5\) data points in the upper half, the upper quartile is the \(\frac{5+ 1}{2}=3\) -th value. So \(Q_3=97\)

Answer:

Median: \(61\), Lower quartile: \(48\), Upper quartile: \(97\)