Question

question #14
determine the mean, median and mode of the following data set:
55 60 84 33 49 28 30 40 84 55 84 89 92 29

mean: 60 median: 60 mode: 55 and 84
mean: 58 median: 55 mode: 84
mean: 95 median: 72 mode: 107
mean:58 median: 55 mode: 55

question #15
the sample data provided contains numbers of injuries due to distracted driving for the past 15 months for a certain town.
find the standard deviation for the sample set of data.

injuries due to distracted driving per month
9,074 8,611 6,922 8,065
10,457 7,551 6,985 9,316
5,292 4,299 6,132 9,442
9,570 12,080 9,433

2048.74
2,134.86
1,548.66
2,023.54

Explanation:

Step1: Calculate the mean of the first data set

First, sum up all the numbers in the data set \(55 + 60+84 + 33+49+28+30+40+84+55+84+89+92+29\).

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There are \(n = 14\) data points. The mean \(\bar{x}=\frac{812}{14}=58\).

Step2: Find the median of the first data set

Sort the data set: \(28,29,30,33,40,49,55,55,60,84,84,84,89,92\).
Since \(n = 14\) (even), the median is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+1)\)th values. \(\frac{n}{2}=7\) and \(\frac{n}{2}+1 = 8\). The 7th value is \(55\) and the 8th value is \(55\), so the median \(=\frac{55 + 55}{2}=55\).

Step3: Determine the mode of the first data set

The mode is the value that appears most frequently. The number \(84\) appears \(3\) times and \(55\) appears \(2\) times. So the mode is \(84\).

Answer:

Mean: \(58\), Median: \(55\), Mode: \(84\) (corresponding to the second option in Question #14)