Questions: Find the mean, ( barx ), of the data. 3,4,5,7,10,12,15 ( overlinemathrmx=[?] )

Transcript text: Find the mean, $\bar{x}$, of the data. \[ 3,4,5,7,10,12,15 \] \[ \overline{\mathrm{x}}=[?] \]

Solution

Step 1: Sum the data values

Add all the given data points together: \[ 3 + 4 + 5 + 7 + 10 + 12 + 15 \]

Step 2: Calculate the total sum

Compute the sum: \[ 3 + 4 = 7 \\ 7 + 5 = 12 \\ 12 + 7 = 19 \\ 19 + 10 = 29 \\ 29 + 12 = 41 \\ 41 + 15 = 56 \] The total sum is $ 56 $.

Step 3: Count the number of data points

Count the number of values in the dataset: \[ 3, 4, 5, 7, 10, 12, 15 \] There are $ 7 $ data points.

Step 4: Compute the mean

Divide the total sum by the number of data points to find the mean: \[ \bar{x} = \frac{56}{7} = 8 \]

The mean of the data is $ \bar{x} = 8 $.

$\boxed{\bar{x} = 8}$

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