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
Nikitich [7]
3 years ago
7

For each part, compare distributions (1) and (2) based on their medians and IQRs. You do not need to calculate these statistics;

simply state how the medians and IQRs compare. Make sure to explain your reasoning
a. (1) 3,5,6,7,9
(2) 3,5,6,7,20

b. (1) 1,2,3,4,5
(2) 6,7,8,9,10

c. (1) 3,5,6,7,9
(2) 3,5,7,8,9

d. (1) 0,10,50,60,100
(2) 0,100,500,600,1000
Mathematics
1 answer:
umka2103 [35]3 years ago
5 0

Answer:

a) The two distributions have the same median (6) but the 2nd distribution has a larger IQR (9.5 > 4).

b) The two distributions have a different median with distribution 2 having a bigger median (8 > 3), but they both have the same IQR (3).

c) The 2nd distribution has a slightly bigger median (7 > 6) and a slightly bigger IQR (4.5 > 4) than the 1st distribution.

d) The 2nd distribution consists of variables that are way bigger than those of the 1st distribution, hence, the median and IQR of the 2nd distribution are about ten folds of that of the 1st distribution.

Step-by-step explanation:

For any distribution,

The median is the variable at the middle when all the variables in the dsitribution are arranged in ascending or descending order.

The median is the (n+1)/2 th variabke.

where n = size of the distribution or number of variables. For these questions, the sample size is 5, hence, the median will always be the 3rd variable when the variables are arranged in ascending or descending order.

The IQR, known as the inter quartile range is a measure of dispersion for the distribution. Although, it isn't as effective as other measures of dispersion such as the standard deviation because the IQR unlike the the standard deviation isn't responsive to changes in the variables, especially ones at the end of the distribution.

The IQR is simply given mathematically as the third quartile minus the first quartile.

IQR = (Third quartile) - (First quartile)

Third quartile is the 3(n+1)/4 th variable. For a sample of n=5, the third quartile is the 4.5th variable, that is the average of the 4th and 5th variable.

First quartile is the (n+1)/4 th variable. For a sample of n=5, the first quartile is the 1.5th variable, that is the average of the 1st and 2nd variable.

Taking the questions one at a time

a) (1) 3,5,6,7,9

Median = 3rd variable = 6

Third quartile = (7+9)/2 = 8

First quartile = (3+5)/2 = 4

IQR = 8 - 4 = 4

(2) 3,5,6,7,20

Median = 3rd variable = 6

Third quartile = (7+20)/2 = 13.5

First quartile = (3+5)/2 = 4

IQR = 13.5 - 4 = 9.5

The two distributions have the same median (6) but the 2nd distribution has a larger IQR (9.5 > 4).

b) (1) 1,2,3,4,5

Median = 3rd variable = 3

Third quartile = (4+5)/2 = 4.5

First quartile = (1+2)/2 = 1.5

IQR = 4.5 - 1.5 = 3

(2) 6,7,8,9,10

Median = 3rd variable = 8

Third quartile = (9+10)/2 = 9.5

First quartile = (6+7)/2 = 6.5

IQR = 9.5 - 6.5 = 3

The two distributions have a different median with distribution 2 having a bigger median (8 > 3), but they both have the same IQR (3).

c) (1) 3,5,6,7,9

Median = 3rd variable = 6

Third quartile = (7+9)/2 = 8

First quartile = (3+5)/2 = 4

IQR = 8 - 4 = 4

(2) 3,5,7,8,9

Median = 3rd variable = 7

Third quartile = (8+9)/2 = 8.5

First quartile = (3+5)/2 = 4

IQR = 8.5 - 4 = 4.5

The 2nd distribution has a slightly bigger median (7 > 6) and a slightly bigger IQR (4.5 > 4) than the 1st distribution.

d) (1) 0,10,50,60,100

Median = 3rd variable = 50

Third quartile = (60+100)/2 = 80

First quartile = (0+10)/2 = 5

IQR = 80 - 5 = 75

(2) 0,100,500,600,1000

Median = 3rd variable = 500

Third quartile = (600+1000)/2 =800

First quartile = (0+100)/2 = 50

IQR = 800 - 50 = 750

The 2nd distribution consists of variables that are way bigger than those of the 1st distribution, hence, the median and IQR of the 2nd distribution are about ten folds of that of the 1st distribution.

Hope this Helps!!!

You might be interested in
Find inverse of y=1/2x+8
Molodets [167]
F^1(x)=2x-16 To find the interverse interchange the variable and solve for y

8 0
3 years ago
This is a GCSE maths question which i don’t understand.
Tpy6a [65]

Answer:

15

Step-by-step explanation:

7 0
3 years ago
Find the value of X!!!!!!!!
Vera_Pavlovna [14]
Try 116, you add up all the numbers and subtract by 180.
7 0
3 years ago
HELP PLEASE!
Bas_tet [7]

Answer:

27/8

Step-by-step explanation:

3 3/8

you multiply the denominator by the whole number and then add into numerator. so

8 x 3 = 24

           24+ 3 =27

Answer= 27/8

6 0
3 years ago
Read 2 more answers
Mia agrees to borrow a 3-year loan with 4% simple interest to buy a motorcycle.
TiliK225 [7]

Answer:

part a: she borrowed 3,700

part b: she would pay 555 interest

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Other questions:
  • When does a parabola open upward
    11·2 answers
  • What is the area of a rhombus DEFG is DF=9 and EG=12
    12·1 answer
  • Please help!!! Thanks!
    11·1 answer
  • Harry had 15 marbles. For his birthday, his grandmother gave him m more marbles. Which expression shows the total number of marb
    5·1 answer
  • A coin contains 1.25, point grams of nickel and 3.75, point, grams of copper, for a total weight of 5 grams. What percentage of
    15·1 answer
  • A.r < 0, V(r) < 0
    6·1 answer
  • Many places of business will not take a check, but will take a credit card.<br><br> True<br> False
    9·1 answer
  • Graphs of the functions f and g are shown in the xy-plane. For which of the following values of x does f(x) + g(x) = 0?
    14·1 answer
  • In 2006, 67.7 million people subscribed to cable television. In 2013, that number had decreased to 56.7 million. Find the percen
    10·1 answer
  • Tito receives a weekly salary of ​$500 at an appliance store. He also receives a7 ​% commission on the total dollar amount of al
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!