Question

for each year of his 9 - year career, brent recorded the fastest time he ran the 400 - meter sprint, as shown in the stemplot
what is the mean and how can it be interpreted?
the mean is \\( \mu=52.4 \\). over the last 9 years, brents average time was 52.4 seconds.
the mean is \\( \mu = 52 \\). over the last 9 years, brents average time was 52 seconds.
the mean is \\( \bar{x}=52.4 \\). over the last 9 years, brents average time was 52.4 seconds.
the mean is \\( \bar{x}=52 \\). over the last 9 years, brents average time was 52 seconds.
400 - meter times
\\( \

$$\begin{array}{l|ll}4 & 7 & 9 \\\\5 & 0 & 1 & 2 & 2 & 4 & 6 \\\\6 & 1\\end{array}$$

\\)
key: \\( 5 | 4=54 \\) seconds

Explanation:

Step1: List out the data values

From the stemplot, the data values are \(47,49,50,51,52,52,54,56,61\).

Step2: Calculate the mean

The formula for the mean \(\mu=\frac{\sum_{i = 1}^{n}x_{i}}{n}\), where \(n = 9\) (the number of data - points) and \(\sum_{i=1}^{n}x_{i}=47 + 49+50+51+52+52+54+56+61\).

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\(\mu=\frac{472}{9}=\frac{472\div2}{9\div2}=\frac{236}{4.5}\approx52.4\)

Since the data is for the entire population (all 9 - year data of Brent's career), we use the population mean symbol \(\mu\).

Answer:

The mean is \(\mu = 52.4\). Over the last 9 years, Brent's average time was 52.4 seconds. So the first option (The mean is \(\mu=52.4\). Over the last 9 years, Brent's average time was 52.4 seconds) is correct.