Question

1. practice summarizing.

a) fill in the blanks to complete the definition.
in statistics, the mean is the same thing as the ___________.
to find the mean, find the ___ of the data values, and divide by the ___ of data values.
b) write the formula for the mean:

1. practice. summarizing.

use the sigma notation to find the mean of 4, 5, 34, 34, 44, 53.
step 1. start with the data set and the sigma notation formula.
step 2. for this data set, n = _____.
step 3. substitute the sum of the data values for the sigma notation.
step 4. simplify.

Explanation:

Step1: Recall mean - related terms

In statistics, the mean is the same as the average. To find the mean, we find the sum of data values and divide by the number of data values.

Step2: Write general formula for mean

The formula for the mean of a data - set \(x_1,x_2,\cdots,x_n\) is \(\bar{x}=\frac{1}{n}\sum_{i = 1}^{n}x_i\).

Step3: Determine \(n\) for the given data set

The data set is \(4,5,34,34,44,53\). The number of data points \(n = 6\). So the mean formula for this data set is \(\bar{x}=\frac{1}{6}\sum_{i = 1}^{6}x_i\).

Step4: Substitute data values into the formula

\(\bar{x}=\frac{1}{6}(4 + 5+34 + 34+44 + 53)\).

Step5: Calculate the sum in the numerator

\(4+5 + 34+34+44+53=(4 + 5)+(34+34)+(44 + 53)=9+68+97=174\).

Step6: Calculate the mean

\(\bar{x}=\frac{174}{6}=29\).

Answer:

1a) average; sum; number
1b) \(\bar{x}=\frac{1}{n}\sum_{i = 1}^{n}x_i\)
2 Step 2: \(6\)
2 Step 3: \(\bar{x}=\frac{1}{6}(4 + 5+34 + 34+44 + 53)\)
2 Step 4: \(29\)