Question

this list shows the lengths in feet of the 25 longest bridges in the united states.
1010 1470 1600 2000 2800
1053 1495 1632 2150 3500
1200 1596 1750 2150 3800
1207 1600 1800 2300 4200
1380 1600 1850 2310 4260
what two lengths are the median and mode of the bridge data?
a. median: 1600
mode: 1750
c. median: 1750
mode: 1600
b. median: 1750
mode: 2150
d. median: 1600
mode: 1800

Explanation:

Step1: Find the median

• There are \(n = 25\) data points.
• The formula for the position of the median in a sorted data set is \(i=\frac{n + 1}{2}\).
• Substitute \(n = 25\) into the formula: \(i=\frac{25+ 1}{2}=13\).
• Sort the data (already presented in a list - we can count to the 13th value). The 13th value in the sorted list is 1750.

Step2: Find the mode

• The mode is the value that appears most frequently.
• Count the frequency of each value:
• 1010: 1 time
• 1053: 1 time
• 1200: 1 time
• 1207: 1 time
• 1380: 1 time
• 1470: 1 time
• 1495: 1 time
• 1596: 1 time
• 1600: 3 times
• 1632: 1 time
• 1750: 1 time
• 1800: 1 time
• 1850: 1 time
• 2000: 1 time
• 2150: 2 times
• 2300: 1 time
• 2310: 1 time
• 2800: 1 time
• 3500: 1 time
• 3800: 1 time
• 4200: 1 time
• 4260: 1 time
• The value 1600 appears 3 times, more frequently than any other value.

Answer:

C. Median: 1750, Mode: 1600