Question Video: Finding the Mean of Data in a Bar Graph | Nagwa Question Video: Finding the Mean of Data in a Bar Graph | Nagwa

Question Video: Finding the Mean of Data in a Bar Graph Mathematics • First Year of Preparatory School

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At a school, every student belongs to one of four houses, and the houses compete throughout the year to earn points. The graph shows how many points each house had scored at the end of the year. Calculate the mean number of points earned. Describe what the mean represents.

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Video Transcript

At a school, every student belongs to one of four houses, and the houses compete throughout the year to earn points. The graph shows how many points each house had scored at the end of the year. Calculate the mean number of points earned. Describe what the mean represents.

We’re first asked to calculate the mean number of points earned. The mean of a data set is found by dividing the sum of all the values in the data set by how many values there are. Here, that means we need to divide the total number of points earned by the number of houses.

We know that the number of houses is four. To determine the total number of points earned, we need to use the graph. Reading across to the vertical axis, we see that the blue house earned 30 points. The orange house earned 70 points. The pink and green houses earned 50 and 90 points, respectively. The total of these four values is 240. The mean number of points earned is therefore equal to 240 over four, which is 60.

The second part of the question asks us what the mean represents. And to answer this, we need to think about how it was calculated. We took the total number of points earned by all four houses and divided it by four. In other words, we shared the total number of points equally between the four houses. The mean therefore represents the number of points that each house would have earned if the total was the same but all houses had earned the same number of points as each other.

So we’ve completed the problem. We’ve found that the mean number of points earned was 60. And we’ve determined that this is the number of points each house would have earned if they had all earned the same number of points.

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