Question

this list shows how many hours twenty batteries lasted when they ran continually in a flashlight.78 31 47 51 1658 60 10 30 4046 63 65 10 9322 13 47 64 93what is the mean, median, and mode of the battery life data?a. mean: 47median: 46.85mode: 10, 47, 93b. mean: 46.85median: 47mode: 10, 47, 93c. mean: 46.85median: 47mode: noned. mean: 47median: 46.85mode: none

Explanation:

Step1: Calculate the mean

The formula for the mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$.
First, find the sum of the data:

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Since \(n = 20\), the mean \(\bar{x}=\frac{937}{20}=46.85\)

Step2: Calculate the median

Sort the data: \(10,10,13,16,22,30,31,40,46,47,47,51,58,60,63,64,65,78,93,93\)
Since \(n = 20\) (an even number), the median \(M=\frac{x_{\frac{n}{2}}+x_{\frac{n}{2}+1}}{2}\)
\(x_{10} = 47\), \(x_{11}=47\), so \(M=\frac{47 + 47}{2}=47\)

Step3: Calculate the mode

The mode is the value that appears most frequently.
The number \(10\) appears \(2\) times, the number \(47\) appears \(2\) times, and the number \(93\) appears \(2\) times. So the modes are \(10\), \(47\), and \(93\)

Answer:

B. mean: 46.85, median: 47, mode: 10, 47, 93