Problems Involving Mean and Median

1. The following table shows the number of attendees at each of the private dance events hosted by Fenel Arrangements.

$\begin{array}{lccc}\text { Event } & \text { Martha's Moonwalk } & \text { Shirly's Shimmy } & \text { Harry's Hoedown } \\\hline \text { Number of attendees } & 48 & 33 & ?\end{array}$

If the mean of the data set is 41 attendees, find the number of attendees at Harry's Hoedown.

_______ attendees

2. The following data points represent the number of points scored last basketball game by each player on the Dragons basketball team.

$5,8,11,7, ?$

If the mean of the data set is 8 points, find the missing number of points.

_______ points

3. The following table shows last year's revenue for each Herman's Hoagies location.

$\begin{array}{lc}\hline \text { Location } & \text { Revenue (in thousands of dollars) } \\\hline \text { Cedarton } & 121 \\\hline \text { Rimber } & 189 \\\hline \text { Linton } & 147 \\\hline \text { Granton } & ?\end{array}$

If the mean of the data set is 158 thousand dollars, find the revenue for the Granton location.

______ thousand dollars

4. The following data points represent the volume of gas in each race car driver's tank (in liters).

$4,5,13, ?$

If the mean of the data set is 7 L, find the missing volume of gas.

______ L

$\begin{array}{ll}\text { Item } & \text { Cost } \\\hline \text { elephant garlic } & \$ 1.29 \\\text { Italian parsley } & \$ 1.92 \\\text { Kosher salt } & \$ 3.19 \\\text { bulgur wheat } & \$ 3.79 \\\text { matzoh meal } & \$ 3.99 \\\text { Anjou pears } & \$ 4.79 \\\text { tahini } & \$ 5.19 \\\text { mozzarella pearls } & \$ 5.29 \\\text { clam stock } & \$ 5.49 \\\text { rose water } & \$ 6.75 \\\text { beef tongue } & \$ 7.19 \\\text { gorgonzola cheese wheel } & \$ 39.99\end{array}$

How will adding the wheel of cheese affect the mean and median?

Choose 1 answer:

(A) Both the mean and median will increase, but the median will increase by more than the mean.

(B) Both the mean and median will increase, but the mean will increase by more than the median.

(C) The mean will increase, and the median will decrease.

(D) The median will increase, and the mean will decrease.

2. Suzanne owns a small business that employs $5$ other people. Suzanne makes $\$ 100,000$ per year, and the other $5$ employees make between $\$ 40,000$ and $\$ 50,000$ per year.

Suzanne decides to leave the company and keep the other 5 salaries the same.

How will removing Suzanne's salary from the data set affect the mean and median?

Choose 1 answer:

(A) The mean will decrease and the median will increase.

(B) The median will decrease and the mean will increase.

(C) Both the mean and median will decrease, but the median will decrease more than the mean.

(D) Both the mean and median will decrease, but the mean will decrease more than the median.

3. A group of $4$ friends likes to golf together, and each friend keeps track of her all-time lowest score in a single round. Their low scores are all between $90$ and $100$, except for Angie, whose low score is $80$.

Angie then golfs a great round and has a new low score of $75$.

How will decreasing Angie's low score affect the mean and median?

Choose 1 answer:

(A) Both the mean and median will decrease.

(B) The median will decrease, and the mean will stay the same.

(C) The mean will decrease, and the median will stay the same.

(D) The mean will decrease, and the median will increase.

4. A cat gave birth to 3 kittens who each had a different mass between 147 and $159 \mathrm{~g}$. Then, the cat gave birth to a $4^{\text {th }}$ kitten with a mass of $57 \mathrm{~g}$.

$\begin{array}{lc}\hline \text { Kitten } & \text { Mass (in grams) } \\\hline \text { Archer } & 147 \\\hline \text { Nate } & 153 \\\hline \text { Lisa } & 159 \\\hline \text { Bob } & 57 \\\hline \end{array}$

How will the birth of the $4^{\text {th }}$ kitten affect the mean and median?

Choose 1 answer:

(A) Both the mean and median will decrease, but the median will decrease by more than the mean.

(B) Both the mean and median will decrease, but the mean will decrease by more than the median.

(C) Both the mean and median will increase, but the median will increase by more than the mean.

(D) Both the mean and median will increase, but the mean will increase by more than the median.

1. An article reported the ages of $12$ CEOs:

The approximate location of the median is point (A/B/C).

The approximate location of the mean is point (A/B/C).

2. A meteorologist recorded the daily high temperature in their city for $62$ consecutive days. Here are the temperatures:

The approximate location of the median is point (A/B/C).

The approximate location of the mean is point (A/B/C).

3. Researchers asked a sample of $96$ teenagers how much cash they currently had with them. Here is a histogram showing their results:

The approximate location of the median is in interval (A/B/C).

The approximate location of the mean is in interval  (A/B/C).

4. A teacher surveyed $28$ students on how long they each spent on a homework assignment. Here are their responses:

The approximate location of the median is point (A/B/C).

The approximate location of the mean is point (A/B/C).