Experimental Design B/C

Post Reply
Anomaly
Exalted Member
Exalted Member
Posts: 641
Joined: February 17th, 2017, 10:46 am
Division: C
State: PA
Pronouns: She/Her/Hers
Location: probably somewhere crying
Has thanked: 3 times
Been thanked: 8 times

Re: Experimental Design B/C

Post by Anomaly » September 20th, 2018, 5:36 pm

dxu46 wrote:
Jacobi wrote:
dxu46 wrote:
1. at least 3
2. at least 4
Actually, only 3 CVs are needed.
Oh, then they changed it, it was 4 last year.
Yes, if you look at the 2019 season rubric it'll say you only need 3 CVs now
Orefield MS SO 2015-2018, Parkland HS SO 2019-2020
Medal/Ribbon Count
Invitational: 25
Regional: 16
State: 7
y o i n k s
Events: Anatomy and Physiology, Codebusters, Designer Genes, Protein Modeling

Jacobi
Exalted Member
Exalted Member
Posts: 137
Joined: September 4th, 2018, 7:47 am
Has thanked: 0
Been thanked: 0

Re: Experimental Design B/C

Post by Jacobi » September 20th, 2018, 5:37 pm

dxu46 can go.

User avatar
dxu46
Exalted Member
Exalted Member
Posts: 799
Joined: April 11th, 2017, 6:55 pm
Division: C
State: MO
Has thanked: 1 time
Been thanked: 0

Re: Experimental Design B/C

Post by dxu46 » September 20th, 2018, 5:56 pm

You test the affect of running speed on perspiration. You results are, for 4 mph, 67 mL, 69 mL, and 81 mL. For 6 mph, your results are 87, 82, and 91 mL. For 8 mph, your results are 101, 101, and 109 mL. List and calculate at least 6 useful statistics.

(disclaimer: this is a FICTIONAL experiment. The results are highly improbable, and the experiment is unlikely to be done. But the question is about statistics, not ideas.)

Jacobi
Exalted Member
Exalted Member
Posts: 137
Joined: September 4th, 2018, 7:47 am
Has thanked: 0
Been thanked: 0

Re: Experimental Design B/C

Post by Jacobi » September 23rd, 2018, 10:01 am

dxu46 wrote:You test the affect of running speed on perspiration. You results are, for 4 mph, 67 mL, 69 mL, and 81 mL. For 6 mph, your results are 87, 82, and 91 mL. For 8 mph, your results are 101, 101, and 109 mL. List and calculate at least 6 useful statistics.

(disclaimer: this is a FICTIONAL experiment. The results are highly improbable, and the experiment is unlikely to be done. But the question is about statistics, not ideas.)
Do they have to be all different?
1. Mean Perspiration (mL): 4 mph -> 72 mL (= (67 + 69 + 81)/3), 6 mph -> 87 mL, 8 mph -> 104 mL
2. Standard Deviation Perspiration (mL): 4 mph -> [math]\sqrt{\frac{(67-72)^2 + (69 - 72)^2 + (81 - 72)^2)}{3}} =[/math] 7.6 mL, 6 mph -> 4.5 mL, 8 mph -> 4.6 mL
3. Median Perspiration (mL): 4 mph -> [b]Find middle of 3 values in order, that is the second-highest value:[/b] [math]67, \underline{69}, 81[/math] 69 mL, 6 mph -> 87 mL, 8 mph - > 101 mL
4. Range Perspiration (mL): 4 mph -> [math]R = max - min = 81-67 =[/math] 14 mL, 6 mph -> 9 mL, 8mph -> 8 mL.
5. Mean Absolute Deviation (mL): 4 mph -> [math]MAD = \frac{1}{n}\Sigma_i |x_i - \overline{x}| = (|67 - 72.33| + |69 - 72.33| + |81 - 72.33|) / 3 = 5.8 mL[/math], 6 mph -> 3.1 mL, 8 mph -> 3.6 mL
6. Pearson Correlation between Hours and Milliliters: [math]r = \Sigma_i \frac{(x_i - \overline{x})(y_i - \overline{y})}{s_x s_y}[/math]
[math]\overline{x} = 6.00[/math]
[math]\overline{y} = 87.6[/math]
[math]s_y = 40.9[/math]
[math]s_x = 4.9[/math]
.
.
.
[math]r = 0.938[/math]
Last edited by Jacobi on October 14th, 2018, 1:15 pm, edited 1 time in total.

User avatar
dxu46
Exalted Member
Exalted Member
Posts: 799
Joined: April 11th, 2017, 6:55 pm
Division: C
State: MO
Has thanked: 1 time
Been thanked: 0

Re: Experimental Design B/C

Post by dxu46 » September 23rd, 2018, 11:52 am

Jacobi wrote:
dxu46 wrote:You test the affect of running speed on perspiration. You results are, for 4 mph, 67 mL, 69 mL, and 81 mL. For 6 mph, your results are 87, 82, and 91 mL. For 8 mph, your results are 101, 101, and 109 mL. List and calculate at least 6 useful statistics.

(disclaimer: this is a FICTIONAL experiment. The results are highly improbable, and the experiment is unlikely to be done. But the question is about statistics, not ideas.)
Do they have to be all different?
1. Mean Perspiration (mL): 4 mph -> 72 mL (= (67 + 69 + 81)/3), 6 mph -> 87 mL, 8 mph -> 104 mL
2. Standard Deviation Perspiration (mL): 4 mph -> [math]\sqrt{\frac{(67-72)^2 + (69 - 72)^2 + (81 - 72)^2)}{3}} =[/math] 7.6 mL, 6 mph -> 4.5 mL, 8 mph -> 4.6 mL
3. Median Perspiration (mL): 4 mph -> [b]Find middle of 3 values in order, that is the second-highest value:[/b] [math]67, \underline{69}, 81[/math] 69 mL, 6 mph -> 87 mL, 8 mph - > 101 mL
4. Range Perspiration (mL): 4 mph -> [math]R = max - min = 81-67 =[/math] 14 mL, 6 mph -> 9 mL, 8mph -> 8 mL.
5. Mean Absolute Deviation (mL): 4 mph -> [math]MAD = \frac{1}{n}\Sigma_i |x_i - \overline{x}| = (|67 - 72.33| + |69 - 72.33| + |81 - 72.33|) / 3 = 5.8 mL[/math], 6 mph -> 3.1 mL, 8 mph -> 3.6 mL
6. Pearson Correlation between Hours and Milliliters: [math]r = \Sigma_i \frac{(x_i - \overline{x})(y_i - \overline{y}}{s_x s_y}[/math]
[math]\overline{x} = 6.00[/math]
[math]\overline{y} = 87.6[/math]
[math]s_y = 40.9[/math]
[math]s_x = 4.9[/math]
.
.
.
[math]r = 0.938[/math]
:o
Your turn.

Jacobi
Exalted Member
Exalted Member
Posts: 137
Joined: September 4th, 2018, 7:47 am
Has thanked: 0
Been thanked: 0

Re: Experimental Design B/C

Post by Jacobi » September 24th, 2018, 8:28 am

Standard deviation measures what quality of a data distribution?

User avatar
OrigamiPlanet
Member
Member
Posts: 156
Joined: August 6th, 2017, 12:15 pm
Division: C
State: PA
Pronouns: He/Him/His
Has thanked: 2 times
Been thanked: 21 times

Re: Experimental Design B/C

Post by OrigamiPlanet » September 24th, 2018, 12:24 pm

Jacobi wrote:Standard deviation measures what quality of a data distribution?
It measures the average variation that the actual values have from the mean value.
Div. C - Cumberland Valley High School

Events
Astronomy; Codebusters; Dynamic Planet

Howdy partner ;)

Email me for anything! Aliases are HeeYaww and v_v_vle

Jacobi
Exalted Member
Exalted Member
Posts: 137
Joined: September 4th, 2018, 7:47 am
Has thanked: 0
Been thanked: 0

Re: Experimental Design B/C

Post by Jacobi » September 25th, 2018, 6:48 am

OrigamiPlanet wrote:
Jacobi wrote:Standard deviation measures what quality of a data distribution?
It measures the average variation that the actual values have from the mean value.
Not exactly...
Try again.

UTF-8 U+6211 U+662F
Exalted Member
Exalted Member
Posts: 1594
Joined: January 18th, 2015, 7:42 am
Division: C
State: PA
Has thanked: 6 times
Been thanked: 9 times

Re: Experimental Design B/C

Post by UTF-8 U+6211 U+662F » September 25th, 2018, 12:08 pm

Jacobi wrote:
OrigamiPlanet wrote:
Jacobi wrote:Standard deviation measures what quality of a data distribution?
It measures the average variation that the actual values have from the mean value.
Not exactly...
Try again.
Wait, what's wrong with that answer? That's pretty much the intent of a standard deviation. Did you just want the spread of the distribution?

Edit: Also, correcting this because the mismatched parentheses bother me...
Jacobi wrote:
dxu46 wrote:You test the affect of running speed on perspiration. You results are, for 4 mph, 67 mL, 69 mL, and 81 mL. For 6 mph, your results are 87, 82, and 91 mL. For 8 mph, your results are 101, 101, and 109 mL. List and calculate at least 6 useful statistics.

(disclaimer: this is a FICTIONAL experiment. The results are highly improbable, and the experiment is unlikely to be done. But the question is about statistics, not ideas.)
Do they have to be all different?
1. Mean Perspiration (mL): 4 mph -> 72 mL (= (67 + 69 + 81)/3), 6 mph -> 87 mL, 8 mph -> 104 mL
2. Standard Deviation Perspiration (mL): 4 mph -> [math]\sqrt{\frac{(67-72)^2 + (69 - 72)^2 + (81 - 72)^2}{3}} =[/math] 7.6 mL, 6 mph -> 4.5 mL, 8 mph -> 4.6 mL
3. Median Perspiration (mL): 4 mph -> [b]Find middle of 3 values in order, that is, the second-highest value:[/b] [math]67, \underline{69}, 81[/math] 69 mL, 6 mph -> 87 mL, 8 mph - > 101 mL
4. Range Perspiration (mL): 4 mph -> [math]R = max - min = 81-67 =[/math] 14 mL, 6 mph -> 9 mL, 8mph -> 8 mL.
5. Mean Absolute Deviation (mL): 4 mph -> [math]\textrm{MAD} = \frac{1}{n}\Sigma_i |x_i - \overline{x}| = (|67 - 72.33| + |69 - 72.33| + |81 - 72.33|) / 3 = 5.8 mL[/math], 6 mph -> 3.1 mL, 8 mph -> 3.6 mL
6. Pearson Correlation between Hours and Milliliters: [math]r = \Sigma_i \frac{(x_i - \overline{x})(y_i - \overline{y}}{s_x s_y}[/math]
[math]\overline{x} = 6.00[/math]
[math]\overline{y} = 87.6[/math]
[math]s_y = 40.9[/math]
[math]s_x = 4.9[/math]
.
.
.
[math]r = 0.938[/math]
should be
1. Mean Perspiration (mL): 4 mph -> [math]\frac{67+69+81}{3} =[/math] 72 mL, 6 mph -> 87 mL, 8 mph -> 104 mL
2. Standard Deviation Perspiration (mL): 4 mph -> [math]\sqrt{\frac{(67-72)^2 + (69 - 72)^2 + (81 - 72)^2)}{3}} =[/math] 7.6 mL, 6 mph -> 4.5 mL, 8 mph -> 4.6 mL
3. Median Perspiration (mL): 4 mph -> [b]Find middle of 3 values in order, that is the second-highest value:[/b] [math]67, \underline{69}, 81 \Rightarrow[/math] 69 mL, 6 mph -> 87 mL, 8 mph - > 101 mL
4. Range Perspiration (mL): 4 mph -> [math]R = \textrm{max} - \textrm{min} = 81-67 =[/math] 14 mL, 6 mph -> 9 mL, 8mph -> 8 mL.
5. Mean Absolute Deviation (mL): 4 mph -> [math]MAD = \frac{1}{n}\Sigma_i |x_i - \overline{x}| = \frac{|67 - 72.33| + |69 - 72.33| + |81 - 72.33|}{3} =[/math] 5.8 mL, 6 mph -> 3.1 mL, 8 mph -> 3.6 mL
6. Pearson Correlation between Hours and Milliliters: [math]r = \Sigma_i \frac{(x_i - \overline{x})(y_i - \overline{y})}{s_x s_y}[/math]
[math]\overline{x} = 6.00[/math]
[math]\overline{y} = 87.6[/math]
[math]s_y = 40.9[/math]
[math]s_x = 4.9[/math]
.
.
.
[math]r = 0.938[/math]

Jacobi
Exalted Member
Exalted Member
Posts: 137
Joined: September 4th, 2018, 7:47 am
Has thanked: 0
Been thanked: 0

Re: Experimental Design B/C

Post by Jacobi » September 25th, 2018, 3:01 pm

UTF-8 U+6211 U+662F wrote:
Jacobi wrote:
OrigamiPlanet wrote:
It measures the average variation that the actual values have from the mean value.
Not exactly...
Try again.
Wait, what's wrong with that answer? That's pretty much the intent of a standard deviation. Did you just want the spread of the distribution?

Edit: Also, correcting this because the mismatched parentheses bother me...
Jacobi wrote:
dxu46 wrote:You test the affect of running speed on perspiration. You results are, for 4 mph, 67 mL, 69 mL, and 81 mL. For 6 mph, your results are 87, 82, and 91 mL. For 8 mph, your results are 101, 101, and 109 mL. List and calculate at least 6 useful statistics.

(disclaimer: this is a FICTIONAL experiment. The results are highly improbable, and the experiment is unlikely to be done. But the question is about statistics, not ideas.)
Do they have to be all different?
1. Mean Perspiration (mL): 4 mph -> 72 mL (= (67 + 69 + 81)/3), 6 mph -> 87 mL, 8 mph -> 104 mL
2. Standard Deviation Perspiration (mL): 4 mph -> [math]\sqrt{\frac{(67-72)^2 + (69 - 72)^2 + (81 - 72)^2}{3}} =[/math] 7.6 mL, 6 mph -> 4.5 mL, 8 mph -> 4.6 mL
3. Median Perspiration (mL): 4 mph -> [b]Find middle of 3 values in order, that is, the second-highest value:[/b] [math]67, \underline{69}, 81[/math] 69 mL, 6 mph -> 87 mL, 8 mph - > 101 mL
4. Range Perspiration (mL): 4 mph -> [math]R = max - min = 81-67 =[/math] 14 mL, 6 mph -> 9 mL, 8mph -> 8 mL.
5. Mean Absolute Deviation (mL): 4 mph -> [math]\textrm{MAD} = \frac{1}{n}\Sigma_i |x_i - \overline{x}| = (|67 - 72.33| + |69 - 72.33| + |81 - 72.33|) / 3 = 5.8 mL[/math], 6 mph -> 3.1 mL, 8 mph -> 3.6 mL
6. Pearson Correlation between Hours and Milliliters: [math]r = \Sigma_i \frac{(x_i - \overline{x})(y_i - \overline{y}}{s_x s_y}[/math]
[math]\overline{x} = 6.00[/math]
[math]\overline{y} = 87.6[/math]
[math]s_y = 40.9[/math]
[math]s_x = 4.9[/math]
.
.
.
[math]r = 0.938[/math]
should be
1. Mean Perspiration (mL): 4 mph -> [math]\frac{67+69+81}{3} =[/math] 72 mL, 6 mph -> 87 mL, 8 mph -> 104 mL
2. Standard Deviation Perspiration (mL): 4 mph -> [math]\sqrt{\frac{(67-72)^2 + (69 - 72)^2 + (81 - 72)^2)}{3}} =[/math] 7.6 mL, 6 mph -> 4.5 mL, 8 mph -> 4.6 mL
3. Median Perspiration (mL): 4 mph -> [b]Find middle of 3 values in order, that is the second-highest value:[/b] [math]67, \underline{69}, 81 \Rightarrow[/math] 69 mL, 6 mph -> 87 mL, 8 mph - > 101 mL
4. Range Perspiration (mL): 4 mph -> [math]R = \textrm{max} - \textrm{min} = 81-67 =[/math] 14 mL, 6 mph -> 9 mL, 8mph -> 8 mL.
5. Mean Absolute Deviation (mL): 4 mph -> [math]MAD = \frac{1}{n}\Sigma_i |x_i - \overline{x}| = \frac{|67 - 72.33| + |69 - 72.33| + |81 - 72.33|}{3} =[/math] 5.8 mL, 6 mph -> 3.1 mL, 8 mph -> 3.6 mL
6. Pearson Correlation between Hours and Milliliters: [math]r = \Sigma_i \frac{(x_i - \overline{x})(y_i - \overline{y})}{s_x s_y}[/math]
[math]\overline{x} = 6.00[/math]
[math]\overline{y} = 87.6[/math]
[math]s_y = 40.9[/math]
[math]s_x = 4.9[/math]
.
.
.
[math]r = 0.938[/math]
What's wrong is the standard deviation measures the typical, not average, deviation from the mean. It's a fine but critical distinction. What parentheses did you correct?

Post Reply

Return to “2019 Question Marathons”

Who is online

Users browsing this forum: No registered users and 1 guest