1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
german
3 years ago
7

Match the values associated with this data set to their correct descriptions. {6, 47, 49, 15, 43, 41, 7, 36}quartile38.5median11

third quartile10.5the differenceof the largestvalue and themedian45
Advanced Placement (AP)
2 answers:
Elza [17]3 years ago
7 0

First quartile. is 11.     median is 38.5.    third quartile is 45.    the diffrence is 10.5

cluponka [151]3 years ago
4 0
Answers:
1) The first quartile (Q₁) = 11 ;  2) The median = 38.5 ; 
3) The third quartile (Q₃) = 45 ;
4) The difference of the largest value and the median = 10.5 .
_______
Explanation: 

Given this data set with 8 (eight) values:  →  {6, 47, 49, 15, 43, 41, 7, 36};
→Rewrite the values in increasing order; to help us find the median, first quartile (Q,) and third quartile (Q₃) : → {6, 7, 15, 36, 41, 43, 47, 49}.
→We want to find; or at least match; the following 4 (four) values [associated with the above data set] — 38.5, 11, 10, 45 ;

1) The first quartile (Q₁);  2) The median;  3) The third quartile (Q₃); & 
4) The difference of the largest value and the median.

Note: Let us start by finding the "median". This will help us find the correct values for the descriptions in "Numbers 2 & 4" above.
The "median" would be the middle number within a data set, when the values are placed in smallest to largest (or, largest to smallest).  However, our data set contains an EVEN number [specifically, "8" (eight)] values. In these cases , we take the 2 (two) numbers closest to the middle, and find the "mean" of those 2 (two) numbers; and that value obtained is the median.  So, in our case, the 2 (two) numbers closest to the middle are:
"36 & 41".  To get the "mean" of these 2 (two) numbers, we add them together to get the sum; and then, we divide that value by "2" (the number of values we are adding):
→  36 + 41 = 77;  → 77/2 = 38.5 ; → which is the median for our data set; and is a listed value.
→Now, examine Description "(#4): The difference of the largest value and the median"—(SEE ABOVE) ;
→ We can calculate this value.  We examine the values within our data set to find the largest value, "49".  Our calculated "median" for our dataset, "38.5".  So, to find the difference, we subtract: 49 − 38.5 = 10.5 ; which is a given value".
→Now, we have 2 (two) remaining values, "11" & "45"; with only 2 (two) remaining "descriptions" to match;
 →So basically we know that "11" would have to be the "first quartile (Q₁)";  & that "45" would have to be the "third quartile (Q₃)".
→Nonetheless, let us do the calculations anyway.
→Let us start with the "first quartile";  The "first quartile", also denoted as Q₁, is the median of the LOWER half of the data set (not including the median value)—which means that about 25% of the numbers in the data set lie below Q₁; & that about 75% lie above Q₁.). 
→Given our data set:   {6, 7, 15, 36, 41, 43, 47, 49};
We have a total of 8 (eight) values; an even number of values. 
The values in the LOWEST range would be:  6, 7, 15, 36.
The values in the highest range would be:  41, 43, 47, 49.
Our calculated median is: 38.5 .  →To find Q₁, we find the median of the numbers in the lower range. Since the last number of the first 4 (four) numbers in the lower range is "36"; and since "36" is LESS THAN the [calculated] median of the data set, "38.5" ; we shall include "36" as one of the numbers in the "lower range" when finding the "median" to calculate Q₁
→ So given the lower range of numbers in our data set:  6, 7, 15, 36 ;
We don't have a given "median", since we have an EVEN NUMBER of values.  In this case, we calculate the MEDIAN of these 4 (four) values, by finding the "mean" of the 2 (two) numbers closest to the middle, which are "7 & 15".  To find the mean of "7 & 15" ; we add them together to get a sum; 
then we divide that sum by "2" (i.e. the number of values added up);
   → 7 + 15 = 22 ;  → 22 ÷ 2 = 11 ;  ↔ Q₁ = 11.
Now, let us calculate the third quartile; also known as "Q₃".
    Q₃ is  the median of the last half of the higher values in the set, not including the median itself.  As explained above, we have a calculated median for our data set, of 38.5; since our data set contains an EVEN number of values.  We now take the median of our higher set of values (which is Q₃). Since our higher set of values are an even number of values; we calculate the median of these 4 (four) values by taking the mean of the 2 (two) numbers closest to the center of the these 4 (four) values.  This value is Q₃.  →Given our higher set of values:  41, 43, 47, 49 ;  → We calculate the "median" of these 4 (four) numbers; by taking the mean of the 2 (two) numbers in the middle; "43 & 47".
 → Method 1): List the integers from "43 to 47" ;  → 43, 44, 45, 46, 47;
→ Since this is an ODD number of integers in sequential order;
→ "45" is not only the "median"; but also the "mean" of (43 & 47); 
thus, 45 = Q₃; 
→ Method 2):  Our higher set of values:  41, 43, 47, 49 ;
→ We calculate the "median" of these 4 (four) numbers; by taking the
"mean" of the 2 (two) numbers in the middle; "43 & 47";  We don't have a given "median", since we have an EVEN NUMBER of values.  In this case, we calculate the MEDIAN of these 4 (four) values, by finding the mean of the 2 (two) numbers closest to the middle, which are "43 & 47."  To find the mean of "43 & 47"; we add them together to get a sum; then we divide that sum by "2" (i.e. the number of values added);
→ 43 + 47 = 90 ;  → 90 ÷ 2 = 45 ;  → 45 = Q₃ .
You might be interested in
A two-year degree that focuses on the arts, humanities, and social sciences is called an
Ne4ueva [31]
I believe that would be considered an associates degree.
6 0
3 years ago
ASAP HELP
Drupady [299]
E— 2.25 the answer!!!
4 0
3 years ago
Read 2 more answers
One should always learn from _____ past mistakes and avoid them in the future.
STatiana [176]
The answer is their
3 0
3 years ago
Read 2 more answers
You have 60 buttons to make 13 shirts. How many buttons can be sewn on each shirt ​
zubka84 [21]
4 buttons can be sewn on each shirt
3 0
3 years ago
Read 2 more answers
In the 18th century Europe, the leading principles were aristocracy, patriarchy, mercantilism, arranged marriages, legal privile
LUCKY_DIMON [66]

In recent time, the aforementioned issues were replaced with discrimination, slavery and genocide of many Native American. Slavery had been one of the biggest problems in the United States that had rooted to racial discrimination and segregation among the citizens of the country as well as it contributes to genocide to many Native American families that were “civilized” by the current culture.

3 0
3 years ago
Read 2 more answers
Other questions:
  • Which of the following is the most significant contributor to the modern “throw away society”?
    6·1 answer
  • if Road or weather conditions are not good a quadruple B Triple C Double D halve your following distance
    5·1 answer
  • STATISTICS PLEASE HELP
    14·1 answer
  • What is the surface area of the given figure
    15·1 answer
  • How many years in college does it take to get a doctorate degree?
    10·2 answers
  • Please help me loves!!!!!!
    15·2 answers
  • What was the Supreme Court's decision in Gray v.
    13·2 answers
  • NEED THIS ASAP!!! due 11:59 lol
    9·1 answer
  • I need help with this question thank you
    6·2 answers
  • Explain at least two factors that contribute to the development of aggression. Include at least one strategy that can be used to
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!