Question Video: Finding the Median of a Data Set Represented in a Line Plot | Nagwa Question Video: Finding the Median of a Data Set Represented in a Line Plot | Nagwa

Question Video: Finding the Median of a Data Set Represented in a Line Plot Mathematics • First Year of Preparatory School

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Find the median of the set of data represented in this line plot.

04:12

Video Transcript

Find the median of the set of data represented in this line plot.

The number line here goes from two to 14. And the number of crosses represents how many of each value we have. There are four crosses above the number four. Therefore, we have four fours. There are six crosses above the number five, so we have six fives. We have two sixes and two sevens. Continuing this, we have six eights, three nines, two 10s, three 11s, three 12s, six 13s, and three 14s. We know that the median is the middle value when the numbers are in ascending order.

One way to answer this question would be to write all the numbers out from smallest to largest. We would write the number four four times. We would write the number five six times. There would be two sixes and two sevens. The list would continue as shown all the way up to three 14s. There are a total here of 40 values. We could find the middle number by crossing off one from each end, firstly, the highest number and the lowest number. We repeat this by crossing another four and another 14. Crossing off the next 10 smallest numbers and next 10 largest numbers would leave us with the numbers from seven to 11. We could continue this process until we’re left with two middle values, eight and nine.

When there are an even number of values in total, there will always be two middle values. We can then find the median by finding the number that is halfway between them. We do this in this case by adding eight and nine and then dividing the answer by two. Eight plus nine is equal to 17, and half of this is 8.5. Clearly, 8.5 is halfway between eight and nine. Therefore, this is the median of the set of data.

An alternative method here would be to calculate the median position first. The median position can be calculated using the formula 𝑛 plus one divided by two, where 𝑛 is the total number of values. 40 plus one is equal to 41. And dividing this by two gives us 20.5. As 20.5 lies between the integers 20 and 21, we know that the median will be halfway between the 20th and 21st value.

To find the 20th and 21st values, we can work out the running total or cumulative frequency. We do this by adding the number of values we have. Four plus six is equal to 10. Adding another two gives us 12. This means that 12 values are six or lower. Adding another two gives us 14, and adding six gives us 20. This means that there are 20 values that are eight or less. As there are 40 values in total, there must therefore be 20 values that are nine or greater. The 20th value is equal to eight, and the 21st value is equal to nine. Once again, finding the midpoint of these two values gives us a median of 8.5. This method is useful when we have a large number of values as it saves writing out the whole data set.

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