Statistics Game

This Statistics Quiz and Game is a great way to put your skills to the test in a fun environment.

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Statistics Game
Mean, median, and mode are measures of central tendency in statistics that help describe the center of a data set.
Scroll down the page for a more detailed explanation.
This Data Detective game focuses on statistical averages. It includes three modes to practice calculating the Mean (average), Median (middle), and Mode (most frequent) of a data set.

Data Detective

Score: 0 Question: 0

Select Challenge Mode

Choose your investigation:

How to Play the Statistics Game
Here’s how to play:

Start: Each Quiz consists of 10 questions. Choose your mode: Mean, Median, Mode, or Mixed Problems.
Look at the Problem: Work out the problem. (Mean, median, or mode)
Select Your Answer: Select the correct answer.
Check Your Work: If you selected the right answer, it will be highlighted in green. If you are wrong, it will be highlighted in red and the correct answer will be highlighted in green.
Get a New Problem: Click “Next Case” for a new problem.
Your score is tracked, showing how many you’ve gotten right.
Finish Game When you have completed 10 questions, click “Finish Game” to get your final score.

Calculating Mean, Median, and Mode
Mean, median, and mode are measures of central tendency that help describe the center of a data set.
Let’s use the following data set for all calculations:
Data Set: [12, 15, 12, 18, 13, 15, 12, 14]

Mean (The Average)
The Mean (or average) is calculated by summing all the values in the data set and dividing the sum by the total number of values.
Formula
\(\text{Mean} = \frac{\text{Sum of all data values}}{\text{Number of data values (n)}}\)
Calculation Example
Sum the values:
12 + 15 + 12 + 18 + 13 + 15 + 12 + 14 = 111
Count the number of values (n):
There are 8 values in the set.
Divide the sum by n:
Mean = \(\frac{111}{8} = 13.875\)
The Mean of the data set is 13.875.

Median (The Middle Value)
The Median is the middle value in a data set that has been ordered from least to greatest.
Calculation Steps
Order the data set: Arrange the values from smallest to largest.
Original: [12, 15, 12, 18, 13, 15, 12, 14]
Ordered: [12, 12, 12, 13, 14, 15, 15, 18]
Find the middle value:
If n is Odd: The median is the single middle value.
Example: [1, 2, 3, 4, 5] Median is 3.
If n is Even (like our example): The median is the average of the two middle values.
Calculation Example (Even n)
Identify the two middle numbers:
Ordered: [12, 12, 12, 13, 14, 15, 15, 18]
The two middle numbers are 13 and 14.
Calculate the average of the two middle numbers:
Median = \(\frac{13 + 14}{2} = \frac{27}{2} = 13.5\)
The Median of the data set is 13.5.

Mode (The Most Frequent Value)
The Mode is the value that appears most often in the data set.
Calculation Steps
Count the frequency of each value. (Using the ordered list makes this easy.)
Identify the value(s) with the highest frequency.
Calculation Example
Check Frequencies:
12 appears 3 times
13 appears 1 time
14 appears 1 time
15 appears 2 times
18 appears 1 time
Identify the most frequent value:
The number 12 appears the most (3 times).
The Mode of the data set is 12.

Special Cases for Mode
Bimodal: If two numbers appear with the same highest frequency (e.g., 12 appears 3 times and 15 appears 3 times).
No Mode: If all numbers appear only once.

This video gives a clear, step-by-step approach to learn how to use the Statistics Formula.

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