How Do You Calculate Quartiles and Variance from a Stem and Leaf Plot?

[graphicer89]

Hi i need to know a couple of things and i don't know how to get to them...thanks for taking a look over this ...

Stem and leaf...

10 |0
9 |2,4,5
8 | 1,2,7,9
7 | 1,1,3
6 | 1,2,8
5 | 1,5

Mean = 77
Mode = 71
Median = what is the mode? I think its 80 but I am not sure...

What is the Third Quartile and First Quartile of this data??

What is the variance??...How can i get the answer to this?
What is the standard deviation of the scores??...Same thing as above I am really lost on this
...can anyone show me how to do this??

 

[HallsofIvy]

So you have 16 data items ranging from 51 to 100. I did not check your mean- that's the one that requires the most calculation. 71 occurs twice and is the only value that occurs more than once so, yes, that's the mode.

The median is the "halfway" number. Since there are 16 numbers, where does the eighth from the top or eight from the bottom occur? It looks like the eighth number from the bottom is 73 and the eighth number from the top is 81. That's a nuisance- there are an even number of data items and "1/2" way lies between two numbers. You might want to check with your teacher on that since different people use different conventions for a situation like this. I, personally, would use the number exactly half way between 73 and 81, which is 77.

The first and third quartiles are the same thing but using 1/4 instead of 1/2. 1/4 of 16 is four so look for the fourth number from the bottom and 12th from the top. The fourth number from the bottom is 62 and the 12th number from the top is 68. I would say the 1st quartile is 65, but, again, you should check with your teacher for the convention you are to use.

 

[Architeuthis Dux]

Sure, I can definitely help you with a stem and leaf plot. It's a great way to organize and visualize data. To find the mean, you would add up all the numbers and divide by the total number of scores. In this case, it would be (10+9+8+7+6+5)/6, which equals 7.7. The mode is the most frequently occurring number, which in this case is 1. The median is the middle number when the scores are arranged in order, so in this case it would be (6+7)/2, which equals 6.5.

To find the Third Quartile, you would first need to find the median of the upper half of the data. In this case, the upper half is (8+9+10)/2, which equals 8.5. The Third Quartile is then the median of this upper half, which is 9.

Similarly, to find the First Quartile, you would find the median of the lower half of the data. In this case, the lower half is (5+6+7)/2, which equals 6. The First Quartile is then the median of this lower half, which is 6.

The variance is a measure of how spread out the data is from the mean. To calculate it, you would first find the difference between each score and the mean, square each difference, and then add them all up. In this case, it would be [(10-7.7)^2 + (9-7.7)^2 + (8-7.7)^2 + (7-7.7)^2 + (6-7.7)^2 + (5-7.7)^2]/6, which equals 3.9.

The standard deviation is the square root of the variance. In this case, it would be √3.9, which is approximately 1.97.

I hope this helps you better understand how to find these values in a stem and leaf plot. If you have any further questions, please don't hesitate to ask. I'm happy to help. Good luck!