Question

a softball team is ordering pizza to eat after their tournament. they plan to order cheese pizzas that cost $6 each and four - topping pizzas that cost $10 each. they order c cheese pizzas and f four - topping pizzas. which expression represents the total cost of all of the pizzas they order?
a. 6 + 10
b. c + f
c. 6c + 10f
d. f/6 + c/10
the values of coins in the pockets of several students are recorded. find the mean of the values: 10, 20, 35, 35, 35, 40, 45, 45, 50, 60
a. 10 cents
b. 35 cents
c. 37.5 cents
d. 50 cents
from unit 1
the dot - plot displays the number of hits a baseball team made in several games. the distribution is skewed to the left.
if the game with 3 hits is considered to be recorded in error, it might be removed from the data set. if that happens:
a. what happens to the mean of the data set?
b. what happens to the median of the data set?

Explanation:

Step1: Calculate the mean of coin - values

The formula for the mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. Here, $x = [10,20,35,35,35,40,45,45,50,60]$, $n = 10$, and $\sum_{i=1}^{n}x_{i}=10 + 20+35+35+35+40+45+45+50+60 = 375$. So, $\bar{x}=\frac{375}{10}=37.5$.

Step2: Analyze the effect on the mean when removing a value from the baseball - hits data

Let the original data set of the number of hits be $x_1,x_2,\cdots,x_n$ with mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. If we remove a value $x_j$ (in this case $x_j = 3$), the new mean $\bar{y}=\frac{\sum_{i = 1}^{n}x_{i}-x_j}{n - 1}$. Since $3$ is less than the original mean of the hits data set, removing it will increase the mean.

Step3: Analyze the effect on the median when removing a value from the baseball - hits data

First, arrange the original data set in ascending order. If $n$ is odd, the median is the middle - value. If $n$ is even, the median is the average of the two middle - values. When we remove the value $3$ (assuming the data set has an odd number of elements), the position of the middle - value may or may not change depending on the original size of the data set. But since the data is skewed left and $3$ is a small value, if the original number of data points $n$ is odd, and $3$ is among the smallest values, removing it will not change the median if the new number of data points $n-1$ still has the same middle - value in the ordered list. If $n$ is even, the effect on the median depends on the relative position of the two middle - values in the original and new ordered data sets. In a left - skewed distribution, removing a small outlier like $3$ may not change the median.

Answer:

1. No question provided for this part in the description.
2. c. 37.5 cents
3. a. The mean increases.

b. The median may or may not change.