Measures of spread

• Percentiles


  Finding a percentile means putting your numbers in order and seeing where your number of interest stands. Knowing percentiles helps you understand how much of the data is less than a certain number.

  
  

  middle observation = percentile/100 (n+1)
• The interquartile range​


  Quartiles divide a set of numbers into four equal groups. These groups help us see how the numbers are spread out. They tell us about the range and how much the numbers differ.

  
  

  Quartiles also help us find something called the "interquartile range" or IQR. It shows how much the middle 50% of the numbers spread out.
• 
  

  First Quartile (Q1): This is the number where 25% of the numbers are lower.

  
  

  Second Quartile (Q2): It's also known as the median. It's the middle number when all the numbers are lined up in order.

  
  

  Third Quartile (Q3): This is the number where 75% of the numbers are lower.
• Measure of central tendency


  Measures of central tendency are ways we figure out the middle or typical value in a group of numbers. They're important because they give us one number that shows what the data is generally like.

  
  

  Basically, they help us find out which numbers show up the most or are most common in a group.
• Mean


  The mean is like the typical value of a group of numbers. You find it by adding up all the numbers and then dividing by how many there are.

  
  

  For example, if you have sales numbers for four months: [1000, 1500, 1200, 1300], you add them up (1000 + 1500 + 1200 + 1300) and then divide by 4 to get 1250.
• Mode (Most Common Value)


  The mode is the number that shows up most often in a group of numbers. For instance, if you have sales numbers for four months: [1000, 1500, 1500, 1300], the mode is 1500 because it appears twice, while the others only appear once.
• Median


  The median is the middle value when the numbers are put in order. If there's an odd number of values, the median is just the middle one. If there's an even number, it's the average of the two middle ones. For example, in a set of sales numbers: [1000, 1200, 1300, 1500], the median is 1250.

  
  

  The median is good at handling extreme values, so it's helpful when there are outliers. But it might not show the whole picture, especially if the data is spread out unevenly.
• For Continuous Data


  When you're dealing with continuous data, like heights or weights, you still use mean and median, but you calculate them slightly differently.

  
  

  The mean is called the arithmetic mean and is found by adding up all the measurements and dividing by how many there are. The median is still the middle value, but it's found by ordering all the measurements first.
• Range


  Range measures the difference between the biggest and smallest numbers in a group.

  
  

  It's easy to find, requiring only two steps: finding the biggest and smallest numbers, and subtracting the smaller one from the bigger one.

  
  

  For instance, finding the range for student heights involves identifying the tallest and shortest students.• However, the range can be affected by extreme values, or outliers, which are very different from the others.

  
  

  Outliers may not provide a true picture of data spread.
• Quartile Ratio


  The quartile ratio helps us see how much data is spread out. It looks at the top 25% of numbers (upper quartile) and the bottom 25% (lower quartile) in a group of numbers.

  
  

  Here's how we calculate it:

  
  

  Quartile Ratio = Upper Quartile (Q3) / Lower Quartile (Q1)

  
  

  The quartile ratio tells us how spread out the numbers are, without needing to know the units. So, it works for any type of data, whether it's money or measurements.
• Decile Ratio


  The decile ratio compares the highest and lowest parts of a group of numbers. It splits the numbers into ten equal groups. The top 10% of the numbers make up the upper decile, and the bottom 10% make up the lower decile.

  
  

  To calculate the decile ratio, you divide the value of the upper decile (the 90th percentile) by the value of the lower decile (the 10th percentile).