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# Center, spread, and shape of distributions — Basic example

Watch Sal work through a basic Center, spread, and shape of distributions problem.

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• the average marks of boys is 68 and that of the girls is 89.if average marks of all is 80,find the ratio of no.of boys to no.of girls
• The answer is 3:4. The explanation is a bit long, but I hope will help you answer similar questions in the future.
We must know that if the number of boys in the class is equal to the number of girls, then the average mark is the average of 68 and 89, which is 78-79 (the computed average is 78.5, but such a number cannot represent students (humans.)) As we see, the average mark in the question is not 78-79 but 80. It means that the number of boys and girls is not the same. Though it's impossible to find the exact number of students in the class based on the information given, we can determine the ratio of the number of boys to girls by finding the difference between 80 and the two average marks, separately. Since 89-80= 9 and 80-68= 12, the ratio is or 3:4. The question arisen is if this ratio is of boys to girls or of girls to boys. To answer this question, you should simply see to which average mark 80 is closer- to this of the boys or of the girls. 80 is closer to 89 than 68, which means there are more girls in the class, so the ratio of girls to boys is 12:9. The question asks for the ratio of boys to girls which is , or 3:4 if simplified. If you want to think about this question in another way, think about a line segment that contain the point A,B and C when B is between A and C. Now imagine that A is placed further from B that C is. It looks like this: .......A..............B.....C....... This exactly the same case in the question you have written.
Hope it helps! Good luck!
• how to you find the center of a distribution?
• You find the middle.
1, 2, 3, 4, 5, 6, 7. The middle is 4.
1, 2, 3, 4, 5, 6, 7, 8. (4+5)÷2=4.5. Median is 4.5.
• What class was this learned in? I have gone through HS Pre-Calc and have NEVER gone over this in school. IIRC the SAT covers Alg I, Geometry, and Alg II, not AP Stats.
• Basic Casework Solves The Problem. Mean, Median and Mode should have been taught in your high school's Finite
• how does Sal teach both math and English ; he is very good at both
• Is there going to be questions involving Standard Deviation in new SAT?
• how to calculate median of a random data
• Order the numbers in the data set from smallest to largest and the middle number is the median. If the data set even then divide the 2 middle numbers to find the median.
• are the videos changed? coz the comments and video are completely mismatched
• Khan Academy does sometimes change the video for a skill if they make an updated version that is more intuitive, and this keeps the old comments the same. However, as far as I know this isn't one of those times, at least in the past 3 years. A lot of comments and questions will talk about their own practice problems that are relevant to the topic in the video, and you might have been confused by those.
• What exactly is the spread definition?
• Someone already answered the same question. Check out imamulhaq's question (should be the second one in the Top Voted) and read its answer. If you still don't get it, feel free to ask. :)