Question

the dot plot shows the number of students who attended the first five meetings of a schools math club.
find the mean of the data.
mean: 9 students
at the next meeting of the club, there are 15 students. how does including this value with the data affect the mean?
the mean? from 9 to? students.

Explanation:

Step1: Calculate the sum of the original data

From the dot - plot, the data points are \(5\) (1 time), \(7\) (2 times), \(13\) (2 times).
The sum of the original data \(S_1=5\times1 + 7\times2+13\times2\)

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The number of data points \(n_1 = 1 + 2+2=5\)

Step2: Calculate the original mean

The formula for the mean \(\bar{x}=\frac{S}{n}\).
The original mean \(\bar{x}_1=\frac{45}{5}=9\)

Step3: Calculate the sum of the new data

The new data point is \(15\). The sum of the new data \(S_2=45 + 15=60\)
The number of data points \(n_2=5 + 1=6\)

Step4: Calculate the new mean

The new mean \(\bar{x}_2=\frac{60}{6}=10\)

Answer:

The mean increases from \(9\) to \(10\) students.