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Scatterplots — Basic example

Watch Sal work through a basic Scatterplots problem.

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  • blobby purple style avatar for user Ezra
    The best part here is that we didn’t have to draw a line
    (45 votes)
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  • leaf red style avatar for user Abhinav Kulhari
    How do we create the best fit line, as sometimes it is not given in the questions.
    (7 votes)
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  • marcimus pink style avatar for user Katelyn  Tran
    Why do you always have to draw the best fit line to determine the answer ?
    (4 votes)
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    • purple pi purple style avatar for user doctorfoxphd
      Lucky for us, in this case, WE didn't have to draw the line of best fit--it was given to us.
      If we don't have a line of best fit, how do we find the rate of change? Well, that would be how much the data increases between points, divided by the measurement increase along the x-axis, which in this case is years.

      But then we have to choose points to use to find the rate of change.
      Here are some of the coordinates from that graph that we can use:

      0 42
      1 46
      2 48
      3 54
      4 47
      5 48
      6 56
      7 58
      8 54
      9 50

      If we choose 0 years and 1 year, the percentages are 42 and 46
      The calculation is (46 - 42)/(1 - 0) which is 4/1 or 4% per year

      If we choose 1 year and 4 years, the percentages are 46 and 47
      The calculation is (47 - 46)/(4 - 1) which is 1/3 or 0.33% per year

      If we choose 3 years and 4 years, the percentages are 54 and 47
      The calculation is (47 - 54)/(4 - 31) which is -7/1 or -7.0% per year

      If we choose 2 years and 5 years, the percentages are 48 and 48
      The calculation is (48 - 48)/(5 - 2) which is 0/3 or 0% per year (no change)

      If we choose 0 years and 9 years, the percentages are 42 and 50
      The calculation is (50 - 42)/(9 - 0) which is 8/8 or 1% per year
      4% .33% -7% 0% 1% are all correctly calculated from the data points, but they are wildly different and none of them is a good answer. THAT is why we draw a line of best fit.

      In other words, we use the slope of an imaginary line that passes through the points to help us choose good points for calculating the answer.
      (20 votes)
  • starky ultimate style avatar for user Brian
    In this case, the vertical axis is already in percents (Percentage of U.S. adults that have this opinion), while the horizontal axis is in years, so percents are already there in the problem. So this is not about calculating percentage based on numbers of people.

    Instead, we need to find the average yearly change in percentage. That is a rate of change problem, so we need to find the amount the vertical height of the data points is changing for every increase in the horizontal axis. To find our the rate of change, we calculate the slope of the line that is closest to all the points, running at about the same slope as the group of points. That is the line of best fit.

    It is best not to choose two points that are really close together, and your result will be most accurate if you find a point that is exactly at the crossing of two grid marks AND on the line of best fit.
    Sal chose to look at the percentage at 1 year and at 9 years. The y- coordinates were 45 and 55 and those are in percent, remember.
    To calculate the slope, (55-45)% is the amount the vertical height changed and the length of time in years was 9 - 1 = 8 years.

    So the slope of the line is 10/8 percent per year which is 5/4 % per year or about 1.25% per year. Because we are using a line of best fit and the scale of the vertical axis is large, this answer is a little off of the alternatives we are given. Two alternatives are silly because they show a negative slope, but our data is definitely increasing. Therefore it is clear which result is correct.

    Hope that helps.
    (6 votes)
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  • blobby green style avatar for user Riley Rivera
    how do we create the best fit line?
    (2 votes)
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    • starky tree style avatar for user Praying Mantis
      Usually they provide the best fit line, but it's basically a straight line as close as possible to as many of the points as possible. Sometimes the best-fitting line is CLEARLY not straight, in that case you draw a parabola, which is a uniform curved line, as close as possible to the points. I hope that helps :)
      (5 votes)
  • aqualine seed style avatar for user noah.popplewell
    how to get the slope on a scatter plot
    (0 votes)
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    • piceratops ultimate style avatar for user Hecretary Bird
      For a scatterplot on the SAT, the fastest and easiest way to get a line of best fit is to just eyeball it. The answers will be different enough from each other that errors will be slight and you can pick the closest answer. Just draw a line through the "center" of the scatterplot, or if you prefer, through the furthest-apart two points that you can find that aren't obvious outliers. Then you can calculate the slope through rise-over-run.
      (11 votes)
  • blobby green style avatar for user Cole Newland
    When given a scatterplot without the line of best fit already provided for you what is the best approach to take to find that line and the slope for that line.
    (1 vote)
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  • piceratops seed style avatar for user eliana9243
    does this count has the statistics part of the sat?
    (2 votes)
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  • blobby green style avatar for user ritika.elen
    how did you get 1.25 from 10%/8
    (1 vote)
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  • blobby green style avatar for user Allie  Eike
    How did you get the 1.25?
    (1 vote)
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Video transcript

- [Presenter] We're told the figure above shows the percent of US adults who are smokers from 1980 to 2000. A line of best fit is also shown. Based on the line of best fit, which of the following is closest to the predicted percent of US adults who are smokers in 1981. And here are our choices, so pause this video and have a go at this on your own before we work through it together. Alright, we're trying to find the closest to predicted percent of US adults who are smokers in 1981. So let's see, we're talking about years since 1980 so 1981 would be one year since 1980, so that would be right over there. And let's see what this predicts. Let's draw a vertical line and it looks pretty close to this hash mark right over here, which is at 31-32%. And so when I look at the choices, I see choice D right over there, 32%.