Answer to Question #224170 in Statistics and Probability for Khan

Question #224170
Question Number 03: [05 Marks]
According to the research conducted by the geologists of University of Texas, the temperatures of soil in 0C at 750 meters deep inside the ground on different locations of earth are mentioned below:
68.4 72.3 58.7 48.3 53.8 73.2 37.9 55.4 42.7 84.6 67.4 58.5 92.4 62.5 87.8
Calculate:
(i) Arithmetic Mean
(ii) Median
(iii) Mode
(iv) Variance
(v) Standard Deviation
1
Expert's answer
2021-08-12T17:58:51-0400

Solution:

Arranging these data in ascending order:

37.9, 42.7, 48.3, 53.8, 55.4, 58.5, 58.7, 62.5, 67.4, 68.4, 72.3, 73.2, 84.6, 87.8, 92.4.

n = 15

(i) Arithmetic mean = "\\mu=\\dfrac{37.9+42.7+...+92.4}{15}=64.26"

(ii) Median "=(n+1)^{th}\/2" observation "=16\/2=8^{th}" observation = 62.5

(iii) Mode = None (as all values appeared once)

(iv) Variance :

"\\sigma^{2}=\\dfrac{\\sum_{i=1}^{n}\\left(x_{i}-\\mu\\right)^{2}}{n}\n\\\\\\Rightarrow \\sigma^{2}=\\dfrac{3600.776}{15}\n\\\\\\Rightarrow \\sigma^{2}=\\dfrac{3600.776}{15}\n\\\\\\Rightarrow \\sigma^{2}=240.05173"

(v): Standard deviation"=\\sigma=15.493603"


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment

LATEST TUTORIALS
New on Blog
APPROVED BY CLIENTS