36,42,40,40,42,40 find the median and mode

Hi there! I'm glad I was able to help you!

We are given the data set 36, 42, 40, 40, 42, 40.

The median is usually found in data sets when you re-arrange the numbers in order from least to greatest, and it ends up being the middle number. However, since we have an even amount of numbers here on our data set, we want to simply add the two middle numbers together, and then divide them by two.

I'll still re-arrange the numbers so you can see what I mean.

36, 40, 40, 40, 42, 42

40 + 40 = 80

80 ÷2 = 40

It seemed kind of pointless to look back at, but we've calculated our median for the data set.

Our MEDIAN is 40.

Now, when I think about finding the MODE of a set of numbers, I think of the word 'most'. It's easy for me to remember what 'mode' means in math because in order to find the mode of a data set you're basically calculating the most common number that occurs in the sequence.

Our mode is 40, since it occurs the most in our set.

Keep in mind for the future that there can be more than one mode! In our case though, there is only one.

I hope this helped you figure out what both terms mean, and how to find them! :)

add an image

step-by-step explanation:

the results from a pre-test for students for the year 2000 and the year 2010 are illustrated in the box plot. what do these results tell us about how students performed on the 29 question pre-test for the two years?

if we compare only the lowest and highest scores between the two years, we might conclude that the students in 2010 did better than the students in 2010. this conclusion seems to follow since the lowest score of 8 in 2010 is greater in value than the lowest score of 6 in 2000. also, the highest score of 28 in 2010 is greater in value than the highest score of 27 in 2000.

but the box portion of the illustration gives us more detailed information. the middle bar in each box shows us that the median score of 20 in 2000 is greater in value than the median score of 17 in 2010. further, we note that the box and whiskers divide the illustration into four pieces. each of these four pieces represents the same portion of students. so, the upper half of the students in 2000 scored in the same score range as the upper one-fourth of the students in 2010, see the illustration at a score of 20.

by considering the upper one-fourth, upper half, and upper three-fourths instead of just the lowest and highest scores, we would conclude that the students as a whole did much better in 2000 than in 2010. we would conclude that as a whole the students in 2010 are less prepared than the students in 2000.

in this section, we discuss box-and-whisker plots and the five key values used in constructing a box-and-whisker plot. the key values are called a five-number summary, which consists of the minimum, first quartile, median, third quartile, and maximum.

step-by-step explanation: