Question

the numbers of students in the 8 schools in a district are given below. (note that these are already ordered from least to greatest.) 165, 230, 297, 313, 326, 345, 433, 443 send data to calculator suppose that the number 443 from this list changes to 235. answer the following. (a) what happens to the mean? it decreases by it increases by it stays the same. (b) what happens to the median? it decreases by it increases by it stays the same.

Explanation:

Step1: Calculate the original mean

The formula for the mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. Here, $n = 8$, and $\sum_{i=1}^{8}x_{i}=165 + 230+297+313+326+345+433+443=2552$. So the original mean $\bar{x}_{1}=\frac{2552}{8}=319$.

Step2: Calculate the new mean

The new sum is $2552-443 + 235=2344$. The new mean $\bar{x}_{2}=\frac{2344}{8}=293$. The change in the mean is $319-293 = 26$.

Step3: Analyze the median

The median of a set with $n = 8$ (even number of data - points) is the average of the $\frac{n}{2}$-th and $(\frac{n}{2}+1)$-th ordered data - points.
The original ordered data: $165,230,297,313,326,345,433,443$. The median $M_{1}=\frac{313 + 326}{2}=\frac{639}{2}=319.5$.
The new ordered data: $165,230,235,297,313,326,345,433$. The median $M_{2}=\frac{297+313}{2}=\frac{610}{2}=305$.

Answer:

(a) It decreases by $26$.
(b) It decreases by $14.5$.