@mathematics.proofs 27 September 2020 edited more from that month

Statistics 101: Range, Mode, Median and Mean

*Article by: Tiago Hands,* *https://www.instagram.com/tiago_hands* In this article I'll be providing the definitions of the **four main concepts in basic statistics**, which are **the range**, **mode**, **median** and **mean**. Whether you're studying GCSE or **A Level mathematics**, these concepts are going to be **foundational in your learning**. The range, mode, median and mean are also used in various job roles such as **accounting**, **investment banking** and **sports analysis**. In fact, it's hard for ordinary people to get by in life without using **averages**. https://www.amazon.co.uk/shop/mathematics.proofs?listId=1U280XC5SGSQU So, below are the four main concepts you need to know before producing any kind of meaningful statistics: The Range The range is simply the **difference between the highest and lowest value** in a data set. Let's say we have the values: 2, 3, 7, 14, 21, 29, 34, 61, 98, 105 What would the range be? Well, the lowest value is 2 and the highest value is 105. This means that the range would have to be 105-2=103. Formula: **Highest Value - Lowest Value = Range** The Mode The mode is the value that **occurs most often** in a data set. If we have the values: 2, 3, 9, 5, 6, **7**, **7**, 4, 15, 21, **7**, **7**, 8, **7**, 3, 1 We'd have to say that 7 is the mode. That is because it appears the most. If however we have the values: **2**, 3, **2**, 7, 7, **9**, **9**, **2**, 8, **9**, 10, 11, 12 We'd have to call our data set ****bimodal****. This is because the values 2 and 9 appear the most often and each 3 times. If all the numbers in a data set **appear as often as each other**, there is ****no mode****. The Median If you put a data set **in order** and obtain the **middle value**, what you'll get is the median. So for instance, if we put this data set in order: 1, 5, 6, 2, 3, 7, 9, 10, 12, 15, 14, 13, 18, 21, 19 --> **1**, **2**, **3**, **5**, **6**, **7**, **9**, **10**, **12**, **13**, **14**, **15**, **18**, **19**, **21** We'd have to call the median 10, as it's the **middle value**. It sits in **position 8** out of 15 ordered numbers. There is a **formulaic way** to get the median value of an ordered data set. Get the number of observations that exist (n), in this case 15, then divide by 2. If n/2 is ****not whole****, then **round your result up and get the corresponding value**. With the data set we're dealing with n/2 would yield the result 7.5. So we'd say that the median value is the 8th term. Once again the median would end up being 10 based on the set of values above. So, what would happen if n/2 ****is whole****? Say we have the ordered data set: 1, 2, 3, 4, **5**, **6**, 7, 8, 9, 10 There are 10 observations so n/2 would be equal to 5. Since 5 is whole, we'd have to get the middle value between the 5th and 6th term. The middle value between 5 and 6 is 5.5, therefore in this case the median would be 5.5. This is the same as (5+6)/2. Let's try out another data set: 1, 4, 5, **7**, **9**, 12, 13, 17 Here there are 8 observations - in order. 8/2 is equal to 4. Since 4 is whole, we have to find the **mid-point** between the 4th and 5th value. That would be (7+9)/2=8. The median in this case would be 8. The Mean The mean is equal to the **sum of observations (Σ)** **divided** by the **total number of observations (n)**. With the data set below (x), what would the mean be? x = {1, 2, 5, 7, 9, 12, 15, 18, 35, 36, 49} n = 11 Well, the sum of observations (Σx) is: Σx = 1 + 2 + 5 + 7 + 9 + 12 + 15 + 18 + 35 + 36 + 49 = 189 And there are 11 observations (n=11), so: (Σx)/n = 189/11 = 17.18 (to 2 decimal places) Therefore in this case, the mean would be 17.18 **to 2 decimal places**. **Video related to this article:** https://youtu.be/eFI5yeu1KqE **I hope this article will be of massive use to you**. Since I'm always dealing with data, using the **range**, **mode**, **median** and **mean** is just natural to me. I've been quite good at mathematics my entire life and I really can't remember a day when I didn't use **at least one type** of average. **For more content like this, subscribe to my page:** **https://read.cash/@mathematics.proofs** I can also be found on Instagram at: **Tiago Hands:** **https://www.instagram.com/tiago_hands** **Mathematics Proofs:** **https://www.instagram.com/mathematics.proofs** *Lead image: By* *Colin Behrens* *from Pixabay* https://pixabay.com/users/ColiN00B-346653/?utm_source=link-attribution&utm_medium=referral&utm_campaign=image&utm_content=3068300