Question

when we add the data value 33 to the original set b, the data values in this new data set can be defined as $x_1$, $x_2$, $cdots$, $x_{50}$, and 33. there are now fifty - one data values in the set, so $n = square$. we can now find the mean for the new data set, rounding the final result to two decimal places. recall that we previously determined that $x_1 + x_2+cdots + x_{50}=350$. $\bar{x}_{new}=\frac{x_1 + x_2+cdots + x_{50}+33}{square}=\frac{350 + 33}{square}=square$

Explanation:

Step1: Determine the number of data - points

The new data set has 50 original values ($x_1,x_2,\cdots,x_{50}$) and 1 new value (33), so $n = 51$.

Step2: Calculate the sum of all data - points

We know that $x_1 + x_2+\cdots+x_{50}=350$, and the new sum is $x_1 + x_2+\cdots+x_{50}+33=350 + 33=383$.

Step3: Calculate the mean

The mean $\bar{x}=\frac{x_1 + x_2+\cdots+x_{50}+33}{n}=\frac{383}{51}\approx7.51$.

Answer:

$n = 51$, mean $\approx7.51$