Respuesta :
Answer:
The mean is [tex]\= x = 79.7 [/tex]
The standard deviation [tex]\sigma =7.81[/tex]
Step-by-step explanation:
From the question we are told that
The data given is
Temperature Lower Limit Upper Limit Days
50-59 50 59 2
60-69 60 69 313
70-79 70 79 1419
80-89 80 89 1503
90-99 90 99 319
100-109 100 109 9
Generally the average of each limit is evaluated as
Temperature Lower Limit Upper Limit Average[tex](x_i)[/tex] Days[tex](f_i)[/tex]
50-59 50 59 ( 50 + 59 )/2 =54.5 2
60-69 60 69 (60+69)/2 = 64.5 313
70-79 70 79 (70+79)/2 =74.5 1419
80-89 80 89 (80+89)/2 =84.5 1503
90-99 90 99 (90+99)/2 = 94.5 319
100-109 100 109 (100+109)/2 = 104.5 9
Generally the mean is evaluated as
[tex]\mu = \frac{\sum x_i f_i}{\sum f_i}[/tex]
=> [tex]\mu = \frac{ (54.5 * 2) + (64.5 * 313) +\cdots +(104.5 * 9)}{2 + 313 +\cdots + 9}[/tex]
=> [tex]\= x = 79.7 [/tex]
Generally the standard deviation is evaluated as
[tex]\sigma = \sqrt{ \frac{\sum[ f_i * ( x_i^2 - \= x^2)] }{\sum f_i}}[/tex]
=> [tex]\sigma =\sqrt{ \frac{[2 * [(54.5)^2) - 79.7^2 ]]+[313 *[ (64.5)^2)-79.7^2] +\cdots +[9 *[ (104.5)^2)- 79.7^2] }{2 + 313 +\cdots + 9}}[/tex]
=> [tex]\sigma =7.81[/tex]
The mean and Standard deviation for the given data would be as follows:
μ [tex]= 79.7[/tex]
б [tex]= 7.81[/tex]
Frequency Distribution
Given that,
Temperature Lower Limit Upper Limit Days([tex]f_{i}[/tex])
50-59 50 59 2
60-69 60 69 313
70-79 70 79 1419
80-89 80 89 1503
90-99 90 99 319
100-109 100 109 9
Average([tex]x_{i}[/tex])
[tex]( 50 + 59 )/2 =54.5[/tex]
[tex](60+69)/2 = 64.5[/tex]
[tex](70+79)/2 =74.5[/tex]
[tex](80+89)/2 =84.5[/tex]
[tex](90+99)/2 = 94.5[/tex]
[tex](100+109)/2 = 104.5[/tex]
As we know,
Mean (μ) [tex]=[/tex] ∑[tex](x_{i} f_{i}) /[/tex]∑[tex]f_{i}[/tex]
[tex]= [(54.5[/tex] × [tex]2) + (64.5[/tex] ×[tex]313)+....(104.5[/tex]× [tex]9)][/tex][tex]/(2 + 313 + 1419 + ....9)[/tex]
∵ μ [tex]= 79.7[/tex]
As we know,
Standard Deviation:-
[tex]\sigma={\sqrt {\frac {\sum(x_{i}-{\mu})^{2}}{f_{i} }}}[/tex]
by putting the values, we get
∵ б [tex]= 7.81[/tex]
Thus, μ [tex]= 79.7[/tex] and б [tex]= 7.81[/tex] are the correct answers.
Learn more about "Temperature" here:
brainly.com/question/7510619
