Question

jorge created a computer program that tracks how many minutes a day his friends spend online. the data below displays the data he gathered.
117.8 97.5 102.1 131.3 111.4
102.9 131.3 131.3 116.2 127.8
what is the mean minutes spent online per day?
mean =
what is the median minutes spent online per day?
median =
what is the mode minutes spent online per day?
mode =

Explanation:

Step1: Sort the data

First, sort the data set: \(97.5, 102.1, 102.9, 111.4, 116.2, 117.8, 127.8, 131.3, 131.3, 131.3\)

Step2: Calculate the mean

The formula for the mean \(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}\). Here \(n = 10\) and \(\sum_{i=1}^{10}x_{i}=97.5 + 102.1+102.9+111.4+116.2+117.8+127.8+131.3+131.3+131.3\)

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\(\bar{x}=\frac{1169.6}{10}=116.96\)

Step3: Calculate the median

Since \(n = 10\) (an even - numbered data set), the median \(M=\frac{x_{\frac{n}{2}}+x_{\frac{n}{2}+1}}{2}\). Here \(\frac{n}{2}=5\) and \(\frac{n}{2}+1 = 6\), \(x_{5}=116.2\), \(x_{6}=117.8\)
\(M=\frac{116.2 + 117.8}{2}=\frac{234}{2}=117\)

Step4: Determine the mode

The mode is the value that appears most frequently. In the data set, \(131.3\) appears \(3\) times, more frequently than any other value.

Answer:

mean \(=116.96\)
median \(=117\)
mode \(=131.3\)