A die is thrown 10 times and obtained the following outputs :
1, 2, 1, 1, 2, 1, 4, 6, 5, 4
What will be the mode of data so obtained ?

Question

A die is thrown 10 times and obtained the following outputs :1, 2, 1, 1, 2, 1, 4, 6, 5, 4 What will be the mode of data so obtained ?

Prepp Team · Accepted Answer

Understanding the Problem: Finding the Mode of Data

The question asks us to find the mode of a given set of data. The data represents the outcomes obtained from throwing a standard die 10 times. We are given the list of these 10 outcomes: 1, 2, 1, 1, 2, 1, 4, 6, 5, 4.

What is the Mode in Statistics?

In statistics, the mode is the value that appears most frequently in a data set. A data set can have one mode (unimodal), more than one mode (multimodal), or no mode if all values appear with the same frequency.

Steps to Find the Mode

To find the mode of the given data, we need to count how many times each distinct number appears in the list of outcomes from the die throws.

The given data set is: 1, 2, 1, 1, 2, 1, 4, 6, 5, 4.

Let's list the distinct values present and count their frequencies:

The number 1 appears in the list. Let's count how many times: 1, 1, 1, 1. It appears 4 times.
The number 2 appears in the list. Let's count how many times: 2, 2. It appears 2 times.
The number 4 appears in the list. Let's count how many times: 4, 4. It appears 2 times.
The number 5 appears in the list. Let's count how many times: 5. It appears 1 time.
The number 6 appears in the list. Let's count how many times: 6. It appears 1 time.

Let's summarize the frequencies in a table:

Outcome	Frequency (Number of Times Appeared)
1	4
2	2
4	2
5	1
6	1

Now, we compare the frequencies to find the highest frequency. The frequencies are 4, 2, 2, 1, and 1. The highest frequency is 4.

The value that corresponds to the highest frequency (4) is the number 1.

Therefore, the mode of the data set 1, 2, 1, 1, 2, 1, 4, 6, 5, 4 is 1.

Conclusion on the Mode of Die Throw Data

Based on our analysis of the frequencies of the outcomes, the number 1 is the mode as it occurred 4 times, which is more frequent than any other outcome in the 10 die throws.

Revision Table: Key Statistical Measures

Measure	Definition	How to Find
Mode	The value that appears most frequently in a data set.	Count the frequency of each distinct value and identify the value(s) with the highest frequency.
Median	The middle value in a data set when the data is ordered from least to greatest.	Order the data. If n is odd, it's the &(\frac{n+1}{2})^{th}& value. If n is even, it's the average of the &(\frac{n}{2})^{th}& and &(\frac{n}{2}+1)^{th}& values.
Mean	The average of all values in a data set.	Sum all values and divide by the total number of values. Formula: &\bar{x} = \frac{\sum x}{n}&

Additional Information: Data Representation

Data obtained from experiments like throwing a die can be represented and analyzed in various ways to understand its characteristics, such as central tendency (mean, median, mode) and spread (range, variance, standard deviation).

Raw Data: The original list of observations as recorded, like the outcomes 1, 2, 1, 1, 2, 1, 4, 6, 5, 4.
Frequency Distribution: A table or graph that shows how often each value or range of values appears in the data set. Our frequency count table above is a simple frequency distribution.
Discrete Data: Data that can only take specific, usually whole, numerical values, like the outcome of a die throw (1, 2, 3, 4, 5, or 6).

Finding the mode is a simple yet useful way to identify the most typical or common outcome in a data set, especially for discrete or categorical data.