Lecture 3.5 - Describing Numerical Data - Percentiles, Quartiles, and Interquartile range

[@dhruvchawla1752]

Explanation: Since many people were having trouble understanding the lecture (took a while for me as well) I have divided into subsections so you can read only the parts you didn't understand. ***100p Percentile*** Percentile basically tells us how many values are more than or less than a given value in a dataset. So, if I say that you got 90 percentile in your class test, I mean that you scored more than or equal to 90 percent people in your class. In this case, p is 0.9 and (1-p) is 0.1, which means 100p is 90 and 100(1-p) is 10. So, the definition makes sense, you got more (or equal) marks than 100p% of your class and less (or equal) than 100(1-p)% of your class. ***How to calculate this *** Now suppose your teacher asks you who scored 75 percentile in your class of 40 students, i.e. which student in your class has more or equal marks as 75% of your class. 1)First thing you will do is to arrange your data in ascending order. 2)Second, you know that 100p is 75, which means p is 0.75 and since your class has 40 students, n is 40. So, now you get np to be equal to 0.75*40 = 30. 3)Third, according to the rules if np is not an integer you find the smallest integer greater than n and the value at that position in the data will be your answer. But, since np is an integer (30), you will take the average of the values at the positions np and np+1 (30 and 31) and that will be your answer. ***Google Sheets Method *** In the video, they chose a dataset of 10 values (n = 10) and then they found the values of 10, 25, 30, 40, 50, 60, 75, 80, 90 and 100 percentiles of the data. Now, for these values, to find p, we divide all of them by 100, so the values of p are 0.1, 0.25, 0.3, 0.4, 0.5, 0.6, 0.75, 0.8, 0.9 and 1. I will only take the example of one of them to explain. Let's say you have to calculate the 25th percentile. The following is the explanation of the process and not the logic behind . 1) First, you arrange the data in ascending order and number them 1, 2, 3....10. Dataset: [35, 38, 47, 58, 61, 66, 68, 68, 70, 79] 1 2 3 4 5 6 7 8 9 10 2) Next, you need to find the rank of 25th percentile, you will do this using the formula rank = p * (n -1) + 1. So, rank = (0.25 x 9) + 1 = 3.25. 3) You then split 3.25 into its integer part (3) and its fractional part (0.25). 4) You set the value of variable i = 3 (the integer part). x[i] represents the value at the position i in the dataset, so that will be the value at position 3 i.e. 47 and so x[1+1] will be the value at position 4 i.e. 58. 5) Now, you substitute the values in the formula: Percentile = x[i] + fractional part * ( x[i + 1] - x[i]) So, your answer for the value of 30th percentile will be: Percentile = 47 + 0.25 * (58-47) = 47 + 2.75 = 49.75 The rest of the video (from 17:30) is easy to understand.

[@agniputhri645]

Thank u so much👍👍

[@Mohammad-ww3nf]

They should hire you instead of this Mam. Well done. Keep it up.

[@captainraman4604]

Damn bro. This was really great. Thanks.

[@kuriakosetcyril4574]

Nice bro👍👍👍

[@kommurilokesh349]

Thank you so much bro😘😄

[@shubhambiswas7904]

Numerical Summaries --> Percentiles ============================================== 0:15 - Percentiles 2:55 - Computing Percentile 6:27 - Example 8:13 - Computing percentile using google sheet 17:24 - Quartiles 19:31 - The Five Number Summary 20:05 - The Interquartile Rang (IQR) 20:55 - Section Summary 22:10 - Module Summary (Added these time stamps for revision)

[@gouravjana7935]

W

[@MuskanKumari-im7jz]

Took me whole day to understand this lecture....thanks to dhruv chawla who explained this concept in comment section.....i also want to contribute to help so here are the explanations 1. What is a Percentile? A percentile is a measure that tells you how a particular score compares to the rest of the group. Specifically, it indicates the percentage of scores in the dataset that are below (or sometimes equal to) a specific value. Example: If you are in the 90th percentile in your class, it means you scored higher than 90% of your classmates. 2. Understanding p in Percentile Calculations In percentile calculations: p represents the percentile rank expressed as a decimal. For example: 90th percentile → p = 0.90 75th percentile → p = 0.75 50th percentile (median) → p = 0.50 100p converts the decimal back to a percentage. For p = 0.75, 100p = 75% 100(1 - p) represents the remaining percentage. For p = 0.75, 100(1 - p) = 25% In summary: p is the percentile as a decimal. 100p% is the percentile in percentage terms. 3. How to Calculate a Percentile Rank Let’s walk through an example to understand how to calculate a percentile rank. Example Scenario: Dataset: Class scores of 40 students. Task: Find the 75th percentile score. Step-by-Step Guide: Step 1: Arrange the Data in Ascending Order First, list all 40 students' scores from lowest to highest. Step 2: Determine p and Calculate np For the 75th percentile: p = 0.75 n is the total number of data points (students). n = 40 Calculate np: np=0.75×40=30 Step 3: Determine the Percentile Position If np is not an integer, round it up to the next whole number. The score at this position is the percentile. If np is an integer, take the average of the scores at positions np and np + 1. example: np = 30, which is an integer. Therefore, the 75th percentile is the average of the scores at positions 30 and 31. Step 4: Find the 75th Percentile Score Locate the 30th and 31st scores in your ordered list. Score at position 30: Let's say it's 85 Score at position 31: Let's say it's 87 Calculate the average: 75 percentile =85+87/2=86 Interpretation: A score of 86 is the 75th percentile. This means you scored higher than or equal to 75% of your class.

[@geetapatidar1382]

Thank you so much for this incredible explanation. God bless you 🙏

[@krishnamsettijayakrishnava3010]

I didn't understand percentile clearly. Please give some more examples to such topics

[@keerthyreddy4288]

Samee

[@shreyamehray4553]

I love this teacher but I just cannot understand this lecture?????

[@karanrana1042]

us

[@subhashkatoch4367]

@@karanrana1042 we 🙃

[@pankajkumarsingh6994]

😢

[@vishalsharma-bg2fg]

Cause you are busy in loving not learning😂

[@deeptigupta4776]

​@@vishalsharma-bg2fg😂😂

[@HimanshuYadav-qy5sm]

I want to meet the people personally who liked the video

[@subhanarayan1195]

True.. One of the most confusing video..

[@ShaswatManojJha]

🤣🤣 Exactly. They are teaching like a revision crash course. While the qualifier was allowing everyone in, i don't think people will survive degree level.

[@raj_patel]

+1

[@teeyeskay1006]

after seeing the comments ,I'm glad that I'm not the only one who is confused 🙂

[@hameeyasmaheenpc2790]

10:28 The Google Sheets algorithms gives a different percentile value (37.5) compared to the value we calculated initially. It raises the question: shouldn't ultimately the percentile value be the same irrespective of the algorithm used? Well turns out there are 2 types of percentile values: Interpolated or Nearest Rank. So by my guess, the first algorithm employs one of these 2 methods and Google Sheets algorithm employs the other.

[@UdaykumarUK-u4r]

Thank you, 🥰

[@gaurav-no1qh]

If anybody have problems to understand these teacher's lacture i have solution you must divided topic in all lectures and visualize it Concepts are very easy but the brain not understand easy concepts so, thank you🙏🙏 all the best

[@Harmansin13]

So which method should we use either the google sheets one or the one you taught ?

[@yourturn_00]

I personally feel that it's confusing to introduce terms like 100p, at least here. Maybe they have some relevance or usefulness later but it would be just so much better if we can keep it more intuitive wherever possible. They could have just said that percentile rank = (number of values below x / N ) * 100. x is the value we want to find the percentile rank of. When we want to find the value which exists at a certain percentile rank, we use: value = percentile*(n+1)/100

[@Dexter4o4]

Simple formula for finding percentile value is =Percentile *(n+1)/100 where n= no. of terms

[@sathishm4594]

But... Answer of 25th percentile is not matching

[@Werner.Heisenberg]

If you can not understand the lecture read the top comment and then watch the lecture

[@sakshi5535]

I think reading the notes of this lecture would be more helpful than learning from her lectures.... sorry but i didn't get anything u taught 👍🙏

[@jainamkhadalia]

where are the notes if you have please send or share link here

[@awierdo69]

Yeah damn right, this lecture basically is about her reading the slides out blindly.

[@mohammedfuzailsirkazi6518]

6:35 Why is np not 10x35=350

[@arushibhagat4810]

Didn't understand anything, sorry.

[@dhruvchawla1752]

I have divided into subsections so you can read only the parts you didn't understand. ***100p Percentile*** Percentile basically tells us how many values are more than or less than a given value in a dataset. So, if I say that you got 90 percentile in your class test, I mean that you scored more than or equal to 90 percent people in your class. In this case, p is 0.9 and (1-p) is 0.1, which means 100p is 90 and 100(1-p) is 10. So, the definition makes sense, you got more (or equal) marks than 100p% of your class and less (or equal) than 100(1-p)% of your class. ***How to calculate this *** Now suppose your teacher asks you who scored 75 percentile in your class of 40 students, i.e. which student in your class has more or equal marks as 75% of your class. 1)First thing you will do is to arrange your data in ascending order. 2)Second, you know that 100p is 75, which means p is 0.75 and since your class has 40 students, n is 40. So, now you get np to be equal to 0.75*40 = 30. 3)Third, according to the rules if np is not an integer you find the smallest integer greater than n and the value at that position in the data will be your answer. But, since np is an integer (30), you will take the average of the values at the positions np and np+1 (30 and 31) and that will be your answer. ***Google Sheets Method *** In the video, they chose a dataset of 10 values (n = 10) and then they found the values of 10, 25, 30, 40, 50, 60, 75, 80, 90 and 100 percentiles of the data. Now, for these values, to find p, we divide all of them by 100, so the values of p are 0.1, 0.25, 0.3, 0.4, 0.5, 0.6, 0.75, 0.8, 0.9 and 1. I will only take the example of one of them to explain. Let's say you have to calculate the 25th percentile. The following is the explanation of the process and not the logic behind . 1) First, you arrange the data in ascending order and number them 1, 2, 3....10. Dataset: [35, 38, 47, 58, 61, 66, 68, 68, 70, 79] 1 2 3 4 5 6 7 8 9 10 2) Next, you need to find the rank of 25th percentile, you will do this using the formula rank = p * (n -1) + 1. So, rank = (0.25 x 9) + 1 = 3.25. 3) You then split 3.25 into its integer part (3) and its fractional part (0.25). 4) You set the value of variable i = 3 (the integer part). x[i] represents the value at the position i in the dataset, so that will be the value at position 3 i.e. 47 and so x[1+1] will be the value at position 4 i.e. 58. 5) Now, you substitute the values in the formula: Percentile = x[i] + fractional part * ( x[i + 1] - x[i]) So, your answer for the value of 30th percentile will be: Percentile = 47 + 0.25 * (58-47) = 47 + 2.75 = 49.75 The rest of the video (from 17:30) is easy to understand.

[@mehulpratapsinghyadav85]

Dhruv Chawla great explanation 💐

[@komaldhumal9353]

Please send link video

[@Muhammed.Yaseen]

All her videos were really great. But really can't understand this particular video. Had to rely on other sources. (still figuring out.)

[@magithaganesamoorthi5468]

So in the exam i should use which algorithm to calculate percentile the first or the second?

[@facts_funday]

She is a AMEZING teacher but i think she have to rush something 😅❤️

[@mercyyy8385]

Yhii sbb agrr hindiii mee smjhaa diyaa hota tohh in sbb lectures ko smjhne me itna time nhi lagta. 😅

[@shubham-vk8fu]

QUALIFIER KA KYA HUA

[@mercyyy8385]

@@shubham-vk8fu that was fine bro

[@fazlunnisha5768]

What if theres no fractional part?

[@quantumgamers69]

Kaun sa Sahi hoga Computer wali ki Solve karne pe

[@vishnupv6867]

np=10 =>not (70+79)/2, but 79 why?

[@amankumardubey]

cause its the maximum value

[@AmitAnjunand]

What is "P" ??

[@AyeshaZubia-yb1rz]

8:00

[@narangtamang5558]

Please remake this video with more better explanation

[@kamleshsolanki230]

Aap sab ka kya kahana hai about this writting

[@MLBB_vaibhav_raj]

What is outliers?

[@sumantkumar7661]

This lecture was lengthy

[@avinash5411]

I dont think its lengthy

[@TheCricketRadio]

Can't clearly understand what is the purpose of calculating measures of dispersion, especially the variance part

[@innovative-minds]

Are median and mode also sensitive to outliers?

[@dhruvchawla1752]

@@TheCricketRadio The reason we calculate measures of dispersion is to be able to see how well the average represents the data. Imagine you have two datasets A = [4, 4, 5, 5] and B = [1, 2, 7, 8] The mean of both A and B is 4.5, but 4.5 represents A better than 4.5 represents B. This is because the values in B are more far apart, you can calculate yourself and verify that B will have higher variance i.e. the values in B are more spread out. This is why we use measures of dispersion.

[@dhruvchawla1752]

@@innovative-minds No, median and mode are not sensitive to outliers. Outliers are values in the data which are on the extremes. Median is a measure of central tendency so the values on the extremes do not have an effect on it. Mode is the value that has the highest frequency in the data. This is also unaffected by outliers.

[@heyanaskhan]

Didn't understand anything 🙂 ! Mam is just focused on google sheets ..

[@SunnySingh-jv5oj]

Kuch samjh nii aaya

[@dhruvchawla1752]

I have divided into subsections so you can read only the parts you didn't understand. ***100p Percentile*** Percentile basically tells us how many values are more than or less than a given value in a dataset. So, if I say that you got 90 percentile in your class test, I mean that you scored more than or equal to 90 percent people in your class. In this case, p is 0.9 and (1-p) is 0.1, which means 100p is 90 and 100(1-p) is 10. So, the definition makes sense, you got more (or equal) marks than 100p% of your class and less (or equal) than 100(1-p)% of your class. ***How to calculate this *** Now suppose your teacher asks you who scored 75 percentile in your class of 40 students, i.e. which student in your class has more or equal marks as 75% of your class. 1)First thing you will do is to arrange your data in ascending order. 2)Second, you know that 100p is 75, which means p is 0.75 and since your class has 40 students, n is 40. So, now you get np to be equal to 0.75*40 = 30. 3)Third, according to the rules if np is not an integer you find the smallest integer greater than n and the value at that position in the data will be your answer. But, since np is an integer (30), you will take the average of the values at the positions np and np+1 (30 and 31) and that will be your answer. ***Google Sheets Method *** In the video, they chose a dataset of 10 values (n = 10) and then they found the values of 10, 25, 30, 40, 50, 60, 75, 80, 90 and 100 percentiles of the data. Now, for these values, to find p, we divide all of them by 100, so the values of p are 0.1, 0.25, 0.3, 0.4, 0.5, 0.6, 0.75, 0.8, 0.9 and 1. I will only take the example of one of them to explain. Let's say you have to calculate the 25th percentile. The following is the explanation of the process and not the logic behind . 1) First, you arrange the data in ascending order and number them 1, 2, 3....10. Dataset: [35, 38, 47, 58, 61, 66, 68, 68, 70, 79] 1 2 3 4 5 6 7 8 9 10 2) Next, you need to find the rank of 25th percentile, you will do this using the formula rank = p * (n -1) + 1. So, rank = (0.25 x 9) + 1 = 3.25. 3) You then split 3.25 into its integer part (3) and its fractional part (0.25). 4) You set the value of variable i = 3 (the integer part). x[i] represents the value at the position i in the dataset, so that will be the value at position 3 i.e. 47 and so x[1+1] will be the value at position 4 i.e. 58. 5) Now, you substitute the values in the formula: Percentile = x[i] + fractional part * ( x[i + 1] - x[i]) So, your answer for the value of 30th percentile will be: Percentile = 47 + 0.25 * (58-47) = 47 + 2.75 = 49.75 The rest of the video (from 17:30) is easy to understand.

[@bsc-itai-01arunsamrat80]

@@dhruvchawla1752 bro the value of p that are we taking is up to us we can take any value

[@komaldhumal9353]

​@@bsc-itai-01arunsamrat80 video link send karo na please

[@RoyAyush13]

what is small p

[@sicksib.]

No introduction, no explanation, just stating the formulas. Nthg special as always , rely from free youtube videos

[@kamleshsolanki230]

Writting is very poor

[@MLBB_vaibhav_raj]

What is outliers ?

[@akashpandey8253]

Kuch samjh nii aaya

[@dhruvchawla1752]

I have divided into subsections so you can read only the parts you didn't understand. ***100p Percentile*** Percentile basically tells us how many values are more than or less than a given value in a dataset. So, if I say that you got 90 percentile in your class test, I mean that you scored more than or equal to 90 percent people in your class. In this case, p is 0.9 and (1-p) is 0.1, which means 100p is 90 and 100(1-p) is 10. So, the definition makes sense, you got more (or equal) marks than 100p% of your class and less (or equal) than 100(1-p)% of your class. ***How to calculate this *** Now suppose your teacher asks you who scored 75 percentile in your class of 40 students, i.e. which student in your class has more or equal marks as 75% of your class. 1)First thing you will do is to arrange your data in ascending order. 2)Second, you know that 100p is 75, which means p is 0.75 and since your class has 40 students, n is 40. So, now you get np to be equal to 0.75*40 = 30. 3)Third, according to the rules if np is not an integer you find the smallest integer greater than n and the value at that position in the data will be your answer. But, since np is an integer (30), you will take the average of the values at the positions np and np+1 (30 and 31) and that will be your answer. ***Google Sheets Method *** In the video, they chose a dataset of 10 values (n = 10) and then they found the values of 10, 25, 30, 40, 50, 60, 75, 80, 90 and 100 percentiles of the data. Now, for these values, to find p, we divide all of them by 100, so the values of p are 0.1, 0.25, 0.3, 0.4, 0.5, 0.6, 0.75, 0.8, 0.9 and 1. I will only take the example of one of them to explain. Let's say you have to calculate the 25th percentile. The following is the explanation of the process and not the logic behind . 1) First, you arrange the data in ascending order and number them 1, 2, 3....10. Dataset: [35, 38, 47, 58, 61, 66, 68, 68, 70, 79] 1 2 3 4 5 6 7 8 9 10 2) Next, you need to find the rank of 25th percentile, you will do this using the formula rank = p * (n -1) + 1. So, rank = (0.25 x 9) + 1 = 3.25. 3) You then split 3.25 into its integer part (3) and its fractional part (0.25). 4) You set the value of variable i = 3 (the integer part). x[i] represents the value at the position i in the dataset, so that will be the value at position 3 i.e. 47 and so x[1+1] will be the value at position 4 i.e. 58. 5) Now, you substitute the values in the formula: Percentile = x[i] + fractional part * ( x[i + 1] - x[i]) So, your answer for the value of 30th percentile will be: Percentile = 47 + 0.25 * (58-47) = 47 + 2.75 = 49.75 The rest of the video (from 17:30) is easy to understand.

[@mationman6822]

@@dhruvchawla1752 thanks for your efforts

[@raj_patel]

@@dhruvchawla1752 Thanks a lot

[@komaldhumal9353]

​@@mationman6822 konsa chanel he please send

[@AmitAnjunand]

What is "P" ??