Question

They want to know the local minimum value and local maximum value

Answer 1

Step-by-step explanation:

I think you mean : YOU want to know the local minimum and maximum values, so that you can answer the question.

we are not doing it for "them", we are doing it for YOU. you are the only one benefiting from the exercise. nobody else. that is why you are supposed to do it.

so, now, focus.

what does that mean : local maximum and local minimum ?

what do you think ?

is the functional value displayed to the right and left of the graph ?

no. the functional value is the y-value to a given x-value and is displayed up and down on the graph.

so, we are looking for some maximum and minimum values in the up/down direction.

where will be the (local) maximum compared to the (local) minimum value ? above or below the minimum value ?

since going up makes the y-value larger, the maximum will be above the minimum, and the minimum will be below the maximum.

are we looking for the overall maximum and minimum ?

no, we are looking for local (that means just in the near neighborhood of the point) maximum and minimum values.

that means that when going left or right of the local maximum value, the curve will go down, but might later go back up again (and then maybe even higher than the maximum we found before).

and when going left or right of the local minimum value, the curve will go up, but might later go back down again (and then maybe even lower than the minimum we found before).

so, look at the graph : where is the curve going up and then suddenly turns around and goes down again ? at what point is that ?

aha, at x = -6 (and the corresponding local maximum y-value = 0). that is our local maximum.

the local maximum value is therefore 0, at the local maximum point (-6, 0).

and at what point is the curve suddenly turning from going down to going up again ?

aha, at x = -2 (and the corresponding local minimum y-value = -8). that is our local minimum.

the local minimum value is therefore -8, at the local minimum point (-2, -8).

to make the difference between local and general maximum/minimum points clearer, the graph indicates that the general maximum is +infinity, and the general minimum is -infinity.

in other words, there are no general maximum and minimum values, as infinity cannot be reached ever. only after infinity, which is not a possible number for any x- value.

Answer 2

The local minimum value is 0 and the local maximum value is 300 within the dataset. The median is the value in the middle when arranged in ascending order, and it is given as 40. To create a box plot, one would use the five number summary which includes the minimum, first quartile, median, third quartile, and maximum value.

Step-by-step explanation:

When discussing the local minimum and local maximum values in a data set or mathematical function, it's important to understand that these values represent the lowest and highest points in a given region or interval. Based on the information provided, the minimum value of the set is 0, and the maximum value is 300. Additionally, the median is stated to be 40, which, since the number of data values is odd, is the middle value when the data is arranged in ascending order. Furthermore, it's mentioned that quartiles can be calculated from a dataset to form a five number summary, which includes the minimum, first quartile, median, third quartile, and maximum value, often used to create a box plot.

To calculate the quartiles and extremes of a dataset using a calculator, such as with the list editor on a graphing calculator, one would enter the data into a list, use the built-in statistical functions to calculate the 1-VarStats, and then extract the needed values like the smallest value, largest value, and the various quartiles.

Graphical representations such as histograms or box-and-whisker plots are also useful tools to depict this information. The histogram can be particularly helpful in identifying the frequency distribution of data, whereas box-and-whisker plots highlight the dispersion and outliers in the data set.