suppose the number 33 is included as an additional data value in set b. compute x for the new data…

suppose the number 33 is included as an additional data value in set b. compute x for the new data - set.\nwe are to determine the mean of the new set that results when the value 33 is included as an additional value in set b. as before, we will first take a closer look at the original set. we are given that set b has n = 50 data values and mean x = 7.\nthere are 50 data values in set b, so we can let x_1, x_2, ..., x_50 be the data values in the original set b. since the mean is equal to 10 we have the following\n\\(\\bar{x}=\\frac{\\sum x}{n}\\)\n\\(7 = \\frac{x_1 + x_2+...+x_50}{50}\\)\n\\((7)=x_1 + x_2+...+x_50\\)\n\\(=x_1 + x_2+...+x_50\\)

suppose the number 33 is included as an additional data value in set b. compute x for the new data - set.\nwe are to determine the mean of the new set that results when the value 33 is included as an additional value in set b. as before, we will first take a closer look at the original set. we are given that set b has n = 50 data values and mean x = 7.\nthere are 50 data values in set b, so we can let x_1, x_2, ..., x_50 be the data values in the original set b. since the mean is equal to 10 we have the following\n\\(\\bar{x}=\\frac{\\sum x}{n}\\)\n\\(7 = \\frac{x_1 + x_2+...+x_50}{50}\\)\n\\((7)=x_1 + x_2+...+x_50\\)\n\\(=x_1 + x_2+...+x_50\\)

Answer

Explanation:

Step1: Find the sum of original data

The formula for the mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. Given $n = 50$ and $\bar{x}=7$, we can find the sum of the original 50 - data values. Cross - multiplying gives $\sum_{i = 1}^{50}x_{i}=n\times\bar{x}=50\times7 = 350$.

Step2: Calculate the sum of new data set

When we add a new data value of 33 to the set, the new sum of data values is $S=350 + 33=383$.

Step3: Compute the new mean

The new number of data values is $n_{new}=50 + 1=51$. The new mean $\bar{x}{new}=\frac{S}{n{new}}=\frac{383}{51}\approx7.51$.

Answer:

$\frac{383}{51}\approx7.51$