Answer to Question #224170 in Statistics and Probability for Khan

Question

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

Answer 1

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 :

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

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