The commute times (in minutes) of 30 employees are listed below. (a) Find Qi, Q3, and the interquartile range (IQR).
(b) Find the fences and determine if there are any outliers in the sample.
20 4 45 48 52 55 56 60 63 65 67 68 6 70 74 75 77 78 79 80 81 82 8 85 87 88 90 92 95 99
Answers
Answer:
Q1 = 54.25 ; Q3 = 82.75 ; IQR = 28.5 ; Outliers = 4, 6, 8
Step-by-step explanation:
Quartiles divide data into 4 equal parts. Q1 has 25% data below it & 75% above it, Q3 has 75% data below it & 25% data above it.
Quartile Calculation for 30 number of observations
- Ascending order : 4, 6, 8, 20, 45, 48, 52, 55, 56, 60, 63, 65, 67, 68, 70, 74, 75, 77, 78, 79, 80, 81, 82, 85, 87, 88, 90, 92, 95, 99
- Q1 = (N + 1) / 4th observation = [ (30 + 1)/4 ] th obs. = (31 /4) th = 7.75th = 7th item + 0.75 (7th - 8th item) = 52 + 0.75 (55-52) = 52 + 0.75(3) = 52 + 2.25 = 54.25
- Q3 = 3 [(N+1) / 4] th observation = 7.75 x 3 = 23.25th item = 23rd item + 0.25 (24th - 23rd item) = 82 + 0.25 (85-82) = 82 + 0.25 (3) = 82 + 0.75 = 82.75
- Interquartile range (IQR) = Q3 - Q1 = 82.75 - 54.25 = 28.5
Outliers are the observations less than Q1 - 1.5 (IQR) , more than Q3 + 1.5 (IQR)
- Q1 - 1.5 (IQR) = 54.25 - 1.5 (28.5) = 54.25 - 42.75 = 11.5 .So, numbers less than 11.5, ie 4, 6, 8 are outliers
- Q3 + 1.5 (IQR) = 82.75 + 1.5 (28.5) = 82.75 + 42.75 = 125.5 .There are no numbers > 125.5
Final answer:
To find Qi, Q3, and the interquartile range (IQR), first, the data needs to be sorted in ascending order. Then, find Q1 as the median of the lower half and Q3 as the median of the upper half. The IQR is the difference between Q3 and Q1. To determine if there are any outliers, calculate the fences using the formulas: Lower fence = Q1 - (1.5 * IQR) and Upper fence = Q3 + (1.5 * IQR). If any commute times fall outside the fences, they are considered outliers.
Explanation:
To find the quartiles, the data needs to be sorted in ascending order. The sorted list is:
4, 6, 8, 20, 45, 48, 52, 55, 56, 60, 63, 65, 67, 68, 70, 74, 75, 77, 78, 79, 80, 81, 82, 85, 87, 88, 90, 92, 95, 99
Q1 is the median of the lower half (ignoring the median if the number of data points is odd), so Q1 = 56.
Q3 is the median of the upper half, so Q3 = 81.
The interquartile range (IQR) is the difference between Q3 and Q1, so IQR = Q3 - Q1 = 81 - 56 = 25.
To find the fences, use the formulas:
Lower fence: Q1 - (1.5 * IQR)
Upper fence: Q3 + (1.5 * IQR)
Lower fence = 56 - (1.5 * 25) = 56 - 37.5 = 18.5
Upper fence = 81 + (1.5 * 25) = 81 + 37.5 = 118.5
There are no commute times that fall outside the fences, so there are no outliers in the sample.
Learn more about quartiles here:
#SPJ3
Related Questions
Find the value of each missing variable.
A school newspaper reporter decides to randomly survey 18 students to see if they will attend Tet festivities this year. Based on past years, she knows that 11% of students attend Tet festivities. We are interested in the number of students who will attend the festivities. Find the probability that more than 2 students will attend.
Multiply the conjugates.(x + 2y)(x - 2y)First to give correct answer gets the brainliest, and hurry please this is timed
Round 34.037 to 3 significant figures. a. 34.04 b. 34 c. 34.037 d. 34.0
(b) What is the probability that the ball chosen from box B is 12 if the arithmetic mean of the three balls selected is exactly 7?
Answers
Answer:
a) 0.73684
b) 2/3
Step-by-step explanation:
part a)
Using conditional probability as above:
(A,B,C)
Cases for numerator when:
P( A is 1 and exactly two balls are 1) = P( 1, not 1, 1) + P(1, 1, not 1)
=
Cases for denominator when:
P( Exactly two balls are 1) = P( 1, not 1, 1) + P(1, 1, not 1) + P(not 1, 1 , 1)
Hence,
Part b
Cases for denominator when:
P ( A + B + C = 21) = P(5,12,4) + P(6,11,4) + P(6,12,3)
Cases for numerator when:
P (B = 12 & A + B + C = 21) = P(5,12,4) + P(6,12,3)
Hence,
Answers
Answer:
$2.06
Step-by-step explanation:
$2.99 x 6 = $17.94
$20.00 - $17.94 = $2.06
Hope this helps
Answer: $0.26
Step-by-step explanation:
Cost of 6 pens
= 2.99 x 6
= 17.94
Add sales tax at 10%,
= 17.94 x 1.1
= 19.74
Change due to me
= 20 - 19.74
= 0.26
Answers
yes it is right triangle
Answers
Answer:
D. F(x) = 2(x-3)^2 + 3
Step-by-step explanation:
We are told that the graph of G(x) = x^2, which is a parabola centered at (0, 0)
We are also told that the graph of the function F(x) resembles the graph of the function G(x) but has been shifted and stretched.
The graph of F(x) shown is facing up, so we know that it is multiplied by a positive number. This means we can eliminate A and C because they are both multiplied by -2.
Our two equations left are:
B. F(x) = 2(x+3)^2 + 3
D. F(x) = 2(x-3)^2 + 3
Well, we can see that the base of our parabola is (3, 3), so let's plug in the x value, 3, and see which equation gives us a y-value of 3.
y = 2(3+3)^2 + 3 =
2(6)^2 + 3 =
2·36 + 3 =
72 + 3 =
75
That one didn't give us a y value of 3.
y = 2(3-3)^2 + 3 =
2(0)^2 + 3 =
2·0 + 3 =
0 + 3 =
3
This equation gives us an x-value of 3 and a y-value of 3, which is what we wanted, so our answer is:
D. F(x) = 2(x-3)^2 + 3
Hopefully this helps you to understand parabolas better.
hundred dollars, would be in the account after 12 years?
Answers
Answer:
A ≈ $500
General Formulas and Concepts:
Pre-Alg
- Order of Operations: BPEMDAS
Algebra I
Compounded Interest Rate: A = P(1 + r/n)ⁿˣ
- A is final amount
- P is initial (principle) amount
- r is rate
- n is number of compounds
- x is number of years
Step-by-step explanation:
Step 1: Define
P = 230
r = 0.063
n = 365
x = 12
Step 2: Solve for A
- Substitute: A = 230(1 + 0.063/365)³⁶⁵⁽¹²⁾
- Divide: A = 230(1 + 0.000173)³⁶⁵⁽¹²⁾
- Multiply: A = 230(1 + 0.000173)⁴³⁸⁰
- Add: A = 230(1.00017)⁴³⁸⁰
- Exponents: A = 230(2.1296)
- Multiply: A = 489.808
Answers
Answer:
- (a) minor arc: XY; major arc: XVY
- (b) XVY = 248°
- (c) tangent: UV; secant: UX
- (d) UV = 6√5
Step-by-step explanation:
(a) Any pair of points on the circle that are separated by less than the diameter will define a minor arc. (The minor arc is the shortest arc of the circle between the points.) Possible minor arcs in this diagram are ...
VX, VY, XY
The corresponding major arc is usually named by adding the name of a point between the two endpoints that is not on the minor arc. For the minor arcs above, the corresponding major arcs are ...
VYX, VXY, XVY
Given that part (b) tells us the minor arc of interest is 112°, we assume that arc is the one subtended by the chord: XY.
Then, per the discussion above, the corresponding major arc is XVY.
___
(b) The sum of major and minor arcs is the whole circle, 360°. So, the measure of the major arc is ...
360° -112° = 248°
___
(c) A tangent line intersects a circle at exactly one point. It is perpendicular to a radius to that point of intersection. The tangent line in this diagram is UV.
A secant intersects a circle in two places. The portion of the secant between the points of intersection is called a chord. The secant line UX contains the chord XY.
___
(d) A rule of secants (and chords) is that the product of distances from where the secants (or chords) meet to the two intersection points with the circle is the same. For a tangent line, effectively, the two points of intersection are at the same distance. This means ...
UV·UV = UX·UY
UV² = 9·(9+11) = 180
UV = √180 = √(6²·5)
UV = 6√5 ≈ 13.42
_____
The attached figure is drawn to scale with arc XY being 112°.
Answer:
(a) minor arc: arc VX
major arc: arc VYX
(b) 248 degrees
(c) Tangent: UV
Secant: UY
Step-by-step explanation:
(b) 360 - 112 = 248
(c) UV crosses on the circumference of the circle at exactly one point
UY crosses through the circle at exactly two points