Question

free response
use the data below for 9–10.
number of vacation days
10 5 9 14 14 12 10 14 12 14

1. find the mean, median and mode of

the data.

Explanation:

Step1: Find the Mean

The mean is calculated by summing all the data points and dividing by the number of data points. The data set is \(5, 9, 10, 10, 12, 12, 14, 14, 14, 14\) (first, we sort the data for easier calculation later, but for the mean, we can sum directly). The sum of the data points is \(5 + 9 + 10 + 10 + 12 + 12 + 14 + 14 + 14 + 14\). Let's calculate that: \(5+9 = 14\), \(14+10 = 24\), \(24+10 = 34\), \(34+12 = 46\), \(46+12 = 58\), \(58+14 = 72\), \(72+14 = 86\), \(86+14 = 100\), \(100+14 = 114\). There are 10 data points, so the mean is \(\frac{114}{10}=11.4\).

Step2: Find the Median

The median is the middle value when the data is sorted. First, sort the data: \(5, 9, 10, 10, 12, 12, 14, 14, 14, 14\). Since there are 10 (an even number) data points, the median is the average of the 5th and 6th values. The 5th value is 12 and the 6th value is 12. So the median is \(\frac{12 + 12}{2}=12\).

Step3: Find the Mode

The mode is the value that appears most frequently. Looking at the sorted data, 14 appears 4 times, which is more than any other value (5 appears 1 time, 9 appears 1 time, 10 appears 2 times, 12 appears 2 times). So the mode is 14.

Answer:

Mean: \(11.4\), Median: \(12\), Mode: \(14\)