sons math question Grade 5

[vfarren82]

Help!!

Instructions: For 12-15, use the stem-and-leaf plot of the test scores.

Table (the table will not show like it is on the paper. The stem ends at the period.
Anything after the period on the table is under Leaves on the table.)

Stem. Leaves
6. 2 6 8
7. 0 1 2 3 4
8. 0 0 2 3 5 8
9. 0 0 0 2 2 4 8

12. What is the median test score?
Median is 5 (the two underlined numbers)

(the question below is the one we couldn't figure out the answer to.
I don't know what formula he is supposed to use to find the answer)
13. Char, Kim, and Denise got the same score on the test.
What was their score?

 

[mmm4444bot]

Stem. Leaves
6. 2 6 8
7. 0 1 2 3 4
8. 0 0 2 3 5 8
9. 0 0 0 2 2 4 8



What is the median test score?

Median is 5 (the two underlined numbers)



I don't know what formula he is supposed to use to find the answer [to the following question].

Char, Kim, and Denise got the same score on the test.

What was their score?

Hi.

The median score is not 5. Nobody got 5 points on the test.

You are misunderstanding the Stem & Leaf plot.



The given plot shows 21 test scores; some scores are in the 60s, some in the 70s, some in the 80s, and the rest are in the 90s.

Each test score is a two-digit number. The stem gives the first digit; the leafs give the second digit.

The first row in the plot is: 6 2 6 8

We see that this row represents three scores: 62, 66, 68



The median is the score in the middle of an ordered list of all 21 scores.

10 + 1 + 10 = 21

Hence, the median score will have 10 scores below it and 10 scores above it.



There is no formula for finding the particular test score that occurs three times in the plot; you just need to hunt for it.

Questions? :cool:

 

[vfarren82]

OMG now that i look at the plot i feel so stupid. I did know that we needed to put the stem number in front of the leaves numbers but we over thought it so much that finding the right answers was so simple we didn't see it. I thought it had to be some formula. And as far as the median thing goes that was my sons teachers mistake. I have been out of school long enough to know that all that median mode and mean stuff don't get used unless you are a math teacher or something that had to do with numbers. She told my son you had to find the two middle numbers and add them together to get the median? If thats not the case then the answer would be 2? Just the number in the middle of the leaves? Or the numbers in the whole plot? I thought you had to use a formula to get the median or at least thats what my son had been taught and up until now getting them right when he added the two middle numbers.

 

[mmm4444bot]

[The teacher] told my son you had to find the two middle numbers and add them together to get the median

If thats not the case then the answer would be 2?

Just the number in the middle of the leaves? Or the numbers in the whole plot?

Examples:

Here is an ordered list of some random numbers:

2 4 17 23 28 37 44

The median is 23 because it is in the middle of the list.

Note that there exists a middle position because the list contains an odd number of entries (there are 7 numbers in the list).



Here is an ordered list that contains an even number of entries (now there are only 6 numbers):

2 4 17 23 28 37

Which number is in the middle? Well, when there are an even number of entries, we see that there exists no middle position.

Here is the rule: when a list contains an even number of entries, the median is the average of the two middle entries.

In this example, the two middle entries are 17 & 23. Hence, the median in this list is 20.

(17 + 23)/2 = 20



Your list of test scores contains 21 entries (that's an odd number of entries), so the median score is the score in the middle position.

As I explained previously, the middle position in your list of 21 scores is the position with 10 scores before it and 10 scores after it.

If you need to, write out the entire ordered list of scores.



Anytime they ask for a score, they don't want just the first digit (the stem); they want the actual score (a two-digit number).

Let us know what they are, if you want us to verify your answers..

Cheers :cool:

 

[JeffM]

I have been out of school long enough to know that all that median mode and mean stuff don't get used unless you are a math teacher or something that had to do with numbers.

Any time you are told on the TV about an average, it is almost undoubtedly a mean. It helps to understand the conceptual difference between a mean and a median.

It is easier to calculate and work numerically with a mean, but the median is usually a more realistic measure of what is typical.

Example Suppose these are annual household incomes (in thousands of dollars) from a random sample of 7 households.

40
55
75
95
100
105
300

\(\displaystyle Median = 95.\)

\(\displaystyle Mean = \dfrac{20 + 55 + 65 + 85 + 100 + 105 + 300}{7} = \dfrac{770}{7} = 110.\)

Notice that only two households are closer to the mean than they are to the median. Five households are closer to the median than to the mean.

Moral: do not put much trust in an "average" unless you are given both the mean and the median.