Mrs. Mojca Conducted A Scrabble Competition With 10 Participants. Use The Following Data To Answer The Questions Below:a. Find The $2^{\text{nd}}$ Quartile.b. Find The $5^{\text{th}}$ Decile.c. Find The $30^{\text{th}}$

by ADMIN 226 views

Mrs. Mojca's Scrabble Competition: Exploring Percentiles and Quartiles

In a recent Scrabble competition conducted by Mrs. Mojca, 10 participants showcased their vocabulary skills. To analyze the performance of the participants, we need to understand and calculate various percentiles and quartiles. In this article, we will delve into the world of percentiles and quartiles, exploring the concepts and applying them to the given data.

Before we dive into the calculations, let's understand the concepts of percentiles and quartiles.

  • Percentiles: A percentile is a measure used in statistics to indicate the value below which a given percentage of observations in a group of observations falls. The most common percentiles are the 25th percentile (also known as the first quartile, Q1), the 50th percentile (also known as the median), and the 75th percentile (also known as the third quartile, Q3).
  • Quartiles: Quartiles are a type of percentile that divides a dataset into four equal parts, each containing 25% of the data. The first quartile (Q1) is the 25th percentile, the second quartile (Q2) is the 50th percentile (median), and the third quartile (Q3) is the 75th percentile.

To calculate the percentiles and quartiles, we need to arrange the data in ascending order.

Rank Score
1 20
2 30
3 40
4 50
5 60
6 70
7 80
8 90
9 100
10 110

a. Find the 2nd Quartile

The 2nd quartile (Q2) is the median of the dataset. To find the median, we need to find the middle value of the dataset. Since there are 10 values in the dataset (an even number), the median will be the average of the 5th and 6th values.

The 5th value is 60, and the 6th value is 70. Therefore, the 2nd quartile (Q2) is the average of 60 and 70.

Q2 = (60 + 70) / 2 Q2 = 65

b. Find the 5th Decile

The 5th decile is the 50th percentile. To find the 50th percentile, we need to find the value below which 50% of the data falls. Since there are 10 values in the dataset, the 50th percentile will be the 5th value.

The 5th value is 60. Therefore, the 5th decile is 60.

c. Find the 30th Percentile

The 30th percentile is the value below which 30% of the data falls. To find the 30th percentile, we need to find the value below which 30% of the data falls.

Since there are 10 values in the dataset, 30% of the data is 3 values. Therefore, the 30th percentile will be the 3rd value.

The 3rd value is 40. Therefore, the 30th percentile is 40.

In conclusion, we have explored the concepts of percentiles and quartiles and applied them to the given data. We calculated the 2nd quartile, 5th decile, and 30th percentile using the given data. The 2nd quartile (Q2) is 65, the 5th decile is 60, and the 30th percentile is 40.

In our previous article, we explored the concepts of percentiles and quartiles and applied them to the data from Mrs. Mojca's Scrabble competition. In this article, we will answer some frequently asked questions related to percentiles and quartiles.

Q: What is the difference between a percentile and a quartile?

A: A percentile is a measure used in statistics to indicate the value below which a given percentage of observations in a group of observations falls. A quartile, on the other hand, is a type of percentile that divides a dataset into four equal parts, each containing 25% of the data.

Q: How do I calculate the median of a dataset?

A: To calculate the median of a dataset, you need to arrange the data in ascending order. If the dataset has an odd number of values, the median will be the middle value. If the dataset has an even number of values, the median will be the average of the two middle values.

Q: What is the 25th percentile?

A: The 25th percentile is also known as the first quartile (Q1). It is the value below which 25% of the data falls.

Q: What is the 75th percentile?

A: The 75th percentile is also known as the third quartile (Q3). It is the value below which 75% of the data falls.

Q: How do I calculate the 50th percentile?

A: The 50th percentile is also known as the median. To calculate the median, you need to find the middle value of the dataset. If the dataset has an odd number of values, the median will be the middle value. If the dataset has an even number of values, the median will be the average of the two middle values.

Q: What is the 30th percentile?

A: The 30th percentile is the value below which 30% of the data falls. To calculate the 30th percentile, you need to find the value below which 30% of the data falls.

Q: What is the 90th percentile?

A: The 90th percentile is the value below which 90% of the data falls. To calculate the 90th percentile, you need to find the value below which 90% of the data falls.

Q: Can I use percentiles and quartiles to compare datasets?

A: Yes, you can use percentiles and quartiles to compare datasets. By comparing the percentiles and quartiles of two or more datasets, you can get an idea of how the data is distributed and whether there are any significant differences between the datasets.

In conclusion, we have answered some frequently asked questions related to percentiles and quartiles. We hope that this article has provided you with a better understanding of these concepts and how to apply them to real-world data.