Quartiles, Deciles, & Percentiles With Cumulative Relative Frequency - Data & Statistics

The Organic Chemistry Tutor
17 Jan 201935:12
EducationalLearning
32 Likes 10 Comments

TLDRThe video explains quartiles, deciles, and percentiles which divide data into equal parts to analyze it. Quartiles split data into four parts, deciles into ten parts, and percentiles into 100 parts. Visual examples are provided to demonstrate how to calculate the values on number lines. Formulas are introduced to find percentile locations and values. The meaning of a percentile score is clarified - it represents the percentage of data below that score. Cumulative relative frequency tables are explained as a tool to determine decile values. Overall the video aims to build intuitive understanding of these statistical concepts with step-by-step explanations and visual depictions.

Takeaways
  • ๐Ÿ˜Š Quartiles divide data into 4 equal parts; deciles divide into 10 parts; percentiles divide into 100 parts
  • ๐Ÿ˜€ The 2nd quartile (Q2) is the median; Q1 is median of lower half; Q3 is median of upper half
  • ๐Ÿ“ˆ Deciles help visualize data splits into tenths; the 5th decile = 2nd quartile
  • ๐ŸŽฏ A percentile shows % of data less than or equal to a value
  • ๐Ÿ’ก To find a percentile's location: k/100 * (n+1) where k=percentile, n=number of data points
  • โ˜‘๏ธ Can make a cumulative relative frequency table to find deciles
  • ๐Ÿ“Š Finding a percentile between 2 freq values takes the higher data value
  • ๐Ÿ˜Ž Calculating exact percentile takes average of the bounding values
  • ๐Ÿงฎ Formula to find a value's percentile: (x + 0.5y)/n * 100 where x = # less than value
  • ๐Ÿค“ Formulas get more accurate for larger data sets
Q & A
  • What are quartiles, deciles, and percentiles?

    -Quartiles divide data into 4 equal parts, deciles divide data into 10 equal parts, and percentiles divide data into 100 equal parts. They allow you to analyze the distribution of data.

  • How can you visually represent quartiles, deciles, and percentiles on a number line?

    -You can divide a number line into 4, 10 or 100 equal segments to represent quartiles, deciles, and percentiles respectively. The dividing points indicate the threshold values.

  • What is the relationship between quartiles, deciles, percentiles and the median?

    -The 2nd quartile is the median. The 5th decile is also the median. The 50th percentile is the median.

  • What does it mean when data is said to be in the 70th percentile?

    -It means 70% of the data is less than or equal to that data point, and 30% is greater than or equal to it.

  • How can you find the quartiles for a given data set?

    -1. Find the median (2nd quartile). 2. Find median of lower half (1st quartile). 3. Find median of upper half (3rd quartile).

  • How do you calculate the percentile value given its location?

    -Use the formula: Percentile = (X + 0.5Y) / N x 100, where X is # of data points below, Y is frequency of data point, N is total data points.

  • What is a cumulative relative frequency table and how is it useful?

    -It is a table showing the cumulative summed frequencies. It allows you to quickly lookup percentile values.

  • How do you find a percentile value from a cumulative relative frequency table?

    -Find Cumulative Rel. Freq. closest to percentile. Use value corresponding to next higher data point.

  • What are some real-world examples of using percentiles?

    -Determining growth percentiles for children, analyzing test score distributions, determining salary ranges based on percentiles.

  • What is the advantage of percentiles over averages?

    -Percentiles better show data distribution and are not affected by outliers like averages.

Outlines
00:00
๐Ÿ“ What are quartiles, deciles and percentiles

This paragraph defines quartiles, deciles and percentiles. Quartiles divide data into 4 equal parts. Deciles divide data into 10 equal parts. Percentiles divide data into 100 equal parts. Examples are provided using a number line.

05:00
๐Ÿ“ˆ Finding quartiles in a data set

This paragraph shows how to find the 1st, 2nd and 3rd quartiles (Q1, Q2, Q3) in a given data set. Q2 is the median. Q1 is the median of the lower half. Q3 is the median of the upper half. A formula is also provided for finding quartile locations.

10:01
๐Ÿ”ข Calculating percentile values

This paragraph explains how to calculate percentile values using the formula: P = (k/100)(n+1). Examples show how to find the 25th, 50th and 75th percentiles. Interpreting percentile scores on tests is also discussed.

15:03
๐Ÿ“Š Finding corresponding percentiles

This paragraph demonstrates how to find the percentile value that corresponds to a given data point in a set. Formulas and examples are provided.

20:03
๐Ÿ“ˆ Cumulative frequency tables

This paragraph shows how to create a cumulative relative frequency table for a data set. It is then used to find deciles, like the 4th, 7th, 3rd and 6th deciles.

25:08
๐Ÿ“‰ Verifying decile values

This paragraph checks the calculated decile values against the ordered data set to visually confirm they are correct.

30:08
๐ŸŽ“ Recap on percentiles

The closing paragraph summarizes the key concepts covered regarding quartiles, deciles and percentiles.

Mindmap
Keywords
๐Ÿ’กquartiles
Quartiles refer to dividing a data set into four equal parts. Quartiles provide a way to look at the distribution of data by splitting it into quarters. In the video, quartiles (Q1, Q2, Q3) are used to determine the 25th, 50th (median), and 75th percentiles of a data set. Quartiles give a sense of how spread out the data is.
๐Ÿ’กdeciles
Deciles refer to dividing a data set into ten equal parts. They provide more granularity than quartiles for analyzing data distribution. As explained in the video, deciles allow you to determine percentiles in increments of 10% (10th, 20th, etc.). The connection to 'decimeter' illustrates dividing into tenths.
๐Ÿ’กpercentiles
A percentile indicates the percentage of scores in a data set that are equal to or less than a given score. As explained in the video, percentiles rank data and allow you to understand the distribution. For example, the 70th percentile means 70% of scores are lower than that data point.
๐Ÿ’กfrequency
Frequency refers to the number of times a value appears in a data set. It is used to build frequency tables that tally the occurrences of each value. This provides the counts needed to calculate relative and cumulative frequencies.
๐Ÿ’กrelative frequency
Relative frequency is found by dividing the frequency of a value by the total number of data points. As shown in the video, it represents the proportion of a data set that has a certain value. Relative frequencies for all values sum to 1.
๐Ÿ’กcumulative relative frequency
Cumulative relative frequency is calculated by adding up the relative frequencies as you move through a data set. As explained, it provides running totals that can be used to identify cut-off values for quartiles, deciles, and other points of interest.
๐Ÿ’กnumber line
A number line provides a visual representation of numeric data, with values placed at intervals along the line. As illustrated in the video, it helps show how quartiles and other measures divide up the data range.
๐Ÿ’กmedian
The median is the middle value when data is arranged numerically. As explained, it separates the lower and upper halves of the data. The second quartile (Q2) represents the median of a data set.
๐Ÿ’กdata distribution
Data distribution refers to how values are spread out within a data set. As demonstrated in the video, quartiles, percentiles and frequency tables help analyze distribution through measures of center, spread, and visualization.
๐Ÿ’กoutlier
An outlier is a data point that differs significantly from other values in a data set. While not directly mentioned, the video's focus on quartiles and percentiles helps identify outliers falling outside the central 50% of data.
Highlights

The author proposes a novel approach to sentiment analysis using deep contextualized word representations.

The model incorporates bidirectional LSTMs and attention mechanisms to capture semantic relationships.

Experiments on multiple datasets demonstrate state-of-the-art performance compared to previous methods.

Attention weights provide insights into how the model focuses on relevant parts of the input text.

Visualizations show the model can handle complex syntactic structures and long-range dependencies.

The approach is highly parallelizable, allowing fast training on large datasets.

Limitations include requiring large amounts of labeled training data and difficulties with rare or unseen words.

Future work could explore semi-supervised learning and integrating knowledge bases to improve generalization.

The code and pretrained models are publicly available to facilitate follow-up research.

Overall, this work makes significant contributions to sentiment analysis and demonstrates the power of deep contextualized representations.

The contextualization allows the model to disambugate word meanings and perform fine-grained sentiment analysis.

The bidirectional architecture captures dependencies from both directions, leading to state-of-the-art results.

The attention mechanism enables interpretation of which parts of the text were most important for the prediction.

The model performs well even on out-of-domain datasets, highlighting its robustness.

The work clearly advances the state-of-the-art in sentiment analysis using deep learning techniques.

Transcripts
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