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In this video, we will learn how to find the range of a data set.
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We will begin by looking at a definition of the range and then answer a variety of questions.
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The range of a data set is the difference between the largest and smallest values.
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We can therefore calculate the range by subtracting the smallest data value from the largest data value.
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The importance of calculating the range is it tells us how spread-out the data is.
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We will now look at some examples to practice finding and using the range.
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The number of goals scored by 12 soccer players in a season are 13, 11, 12, five, five, nine, six, 11, eight, five, six, and 19.
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State whether the following statement is true or false.
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The range of the data is 14 goals.
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We can calculate the range of any set of data by subtracting the smallest value from the largest value.
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Whilst we could find these values from the list by inspection, it is often useful to rewrite the data set in numerical order first.
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The smallest value in the data set is five.
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And there are three of these.
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There are two sixes in the data set.
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The next lowest value is eight.
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Continuing our list from smallest to largest, we have 9, 11, 11, 12, 13, and 19.
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The smallest value is equal to five and the largest value is 19.
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We can therefore calculate the range by subtracting five from 19.
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This is equal to 14.
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The statement in the question said that the range of the data is 14 goals, which is true.
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Our next question involves working out the range from a set of data represented on a line plot.
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The graph shows the weights, in kilograms, of emperor penguins at a zoo.
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Is the range of the weights 24 kilograms?
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The range of any data set can be calculated by subtracting the smallest value from the largest value.
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As the weights on the line plot are already in order, we can see that the smallest value is 23 kilograms.
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The largest value is 49 kilograms.
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We can therefore calculate the range by subtracting 23 from 49.
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40 minus 20 is equal to 20, and nine minus three is equal to six.
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Therefore, 49 minus 23 equals 26.
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The range of values of the emperor penguins is 26 kilograms.
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This means that the answer to the question βIs the range of the weights 24 kilograms?β is no.
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Let the greatest element in a set be 445 and the range of the set be 254.
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What is the smallest element of this set?
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We know that, in order to calculate the range of any set, we subtract the smallest element from the largest element.
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In this question, we are given the largest or greatest element and the range of the set and need to calculate the smallest element.
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We can do this by using the formula or by using the number line.
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Substituting in our values gives us 254 is equal to 445 minus π₯, where π₯ is the smallest element of the set.
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Adding π₯ to both sides of this equation gives us π₯ plus 254 is equal to 445.
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We can then subtract 254 from both sides of this equation to work out the value of π₯.
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π₯ is equal to 191 as 445 minus 254 is 191.
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We can therefore conclude that the smallest element of the set is 191.
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As already mentioned, we could also have calculated this using a number line.
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We know that the greatest value is 445.
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The range is the difference between the greatest or largest value and the smallest value.
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In this case, we are told it is 254.
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The difference between the smallest and greatest value is 254, which means we can subtract this from 445 to calculate the smallest value.
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Once again, this gives us an answer of 191.
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We will now look at a couple of more complicated problems to finish this video.
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The following figure demonstrates the number of glasses of water a group of people consume per day.
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Describe how the range would change if an additional data value of one was added to the data set.
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The graph tells us that eight people consume zero glasses of water per day.
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Five people consume one glass; two people consume two glasses; six people, three glasses; one person, four glasses; and, finally, seven people consume five glasses of water per day.
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We know that, in order to calculate the range of a data set, we subtract the smallest value from the largest value.
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In this question, it will be the number of glasses.
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It doesnβt matter how many different people consume that number of glasses.
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The smallest value is therefore zero.
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As thereβre some people, in this case, eight, that consume no glasses of water.
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The largest value is equal to five as this is the greatest number of glasses of water that anybody consumes.
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We can therefore calculate the range of the original data by subtracting zero from five.
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This is equal to five.
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We are then told that there is an additional data value of one that is added to the data set.
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This means that there are now six people that consumed one glass of water per day.
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This does not impact the smallest or largest value though.
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So the new range is still equal to five minus zero.
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Adding the extra data value does not alter the range.
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We can therefore conclude that the range would remain unchanged at five.
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Michael has the following data: Six, eight, π, eight, eight, and nine.
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If the range is three, which number could π be?
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Is it (A) three, (B) four, (C) five, (D) six, or (E) 13?
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We recall that we can calculate the range by subtracting the smallest value from the largest value.
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In this question, we will consider what the largest value and smallest values are when π takes each of the five options.
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One of these options will have a range of three which will be the correct answer.
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When π is equal to three, our list of values in ascending order are three, six, eight, eight, eight, and nine.
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As the largest value is nine and the smallest value is three, the range will be equal to nine minus three.
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As this is equal to six, option (A) is not correct.
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When π is equal to four, the smallest value is four and the largest value is nine.
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This time the range would be equal to nine minus four, which is equal to five.
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Once again, this is not correct.
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When π is equal to five the smallest number is five.
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The largest number is still nine.
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The range in this case is equal to four, which once again is not correct.
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When π is equal to six, we have two sixes.
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We could write these in either order.
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Our list is now six, six, eight, eight, eight, and nine.
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As the smallest number in this set of date of is six and the largest is nine, the range is equal to nine minus six.
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This is equal to three, which suggests that option (D) is correct.
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We will check option (E) just to make sure.
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This time, π is equal to 13.
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This means that the smallest number is six and the largest number is 13.
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The range is the difference between these values.
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13 minus six is equal to seven.
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So this answer is also incorrect.
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This means that the correct answer is option (D).
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If the range is three, the number from the list that π could be is six.
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There are a few other numbers that were not one of the options that π could be.
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As long as six remains the smallest number and nine remains the largest number, the range will always be three.
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This means that π could be any one of the four integers, six, seven, eight, or nine.
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In this question, the only one of those that was listed as an option was six, which is why this is the only correct answer.
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We will now summarize the key points from this video.
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The range of a data set is the difference between the largest and smallest values.
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We can therefore calculate the range of any data set by subtracting the smallest value from the largest value.
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The range of a set of data tells us how spread-out the data is.
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This means that adding any extra values to a data set doesnβt always change the range.
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For example, letβs consider the data set four, seven, 10, 10, and 13.
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The smallest value here is four, and the largest value is 13.
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This means that the range is equal to nine as 13 minus four equals nine.
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Adding in any extra values between four and 13 inclusive will not affect the range.
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For example, if we added the number eight, the smallest number is still four and the largest number is 13.
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This means that the range is still nine.
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It is also important to note that it doesnβt matter how many of each value we have.
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If we added any extra fours or extra 13s to this list, the range would still be nine.
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As well as using a list of data values, we can also calculate the range from a frequency table or graph.