May 2, 2020

For the first one:


The frequency is how many bags containing each number of apples there are.


The sum of the apple in the first 11 bags would be \((6 * 1)+(7*4)+(8*2)+(9*3)+(10*1)\)

which is \(6+28+16+27+10=87\) total apples in the first 11 bags :D

The formula for the average (mean) is the sum of all the data points divided by the number of data points.


The number of apples in the 12th bag is unknown, so let's call that x.


We know that the sum of all the data points is \(87+x\). That divided by 12 (the number of data points) equals the mean, which, as stated by the question, is \(8\).


So, our equation is that \(\dfrac{87 + x}{12} = 8\) :D

Multiplying the equation by 12 gets us \(87+x=96\).

Now, we can subtract 87 from the equation to get that \(x=96-87=9\).


So, the 12th bag contains \(9\) apples :D

 May 2, 2020
edited by CentsLord  May 2, 2020

For teh second one:


Let's treat 20 as one data point. There are 10 data points less than 20, and 20 data points more than 20.


In case you didn't know, the median is the middlemost number in a data set, when it is arranged from greatest to least.


For example, in the array (1, 3, 5, 7, 9), 5 is the median as it is in the middle. There are 2 numbers to its left, and 2 numbers on its right.

When dealing with arrays that don't have a middlemost number (i.e. having an even number of data points) like (1, 2, 3, 4, 5, 6), we just find the two numbers closest to the middle. Here, the medians would be 3 and 4.


Using this information, could you estimate in which interval the median for the plant set will be? I trust you can! :D

 May 2, 2020

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