Find mean and standard deviation of first 15 natural numbers.
Answers
The formula to calculate SD is SD=∑x2n−(∑xn)2−−−−−−−−−−−−−−√
1st 10 natural numbers are 1,2,3,4,5,6,7,8,9,10
∑x=1+2+3+4+5+6+7+8+9+10
=n(n+1)2=10(10+1)2
=10×112=55
∑x2=12+22+..............+102
=n(n+1)(2n+1)6
=10×11×216
=385
SD=∑x2n−(∑xn)2−−−−−−−−−−−−−−√
=38510−(5510)2−−−−−−−−−−−−√
=38.5−(5.5)2−−−−−−−−−−√
=8.25−−−−√
=2.87
we can calculate 15 natural numbers same as above i have calculated
Answer: -We need to find the mean and standard deviation of first 15 natural numbers. The program for it is written below.
The formula to calculate SD is SD = ∑x2n−(∑xn)2
1st 10 natural numbers are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
∑x = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10
= n(n+1)2 = 10(10+1)2
= 10×112 = 55
∑x2 = 12+22+..............+102
= n(n+1) (2n+1)6
=10×11×216
=385
SD=∑x2n−(∑xn)2
=38510−(5510)2
=38.5−(5.5)2
=8.25
=2.87
The program is: -
import NumPy as np #for declaring an array or simply use list
def mean(data):
n = len(data)
mean = sum(data) / n
return mean
def variance(data):
n = len(data)
mean = sum(data) / n
deviations = [(x - mean) ** 2 for x in data]
variance = sum(deviations) / n
return variance
def stdev(data):
import math
var = variance(data)
std_dev = math.sqrt(var)
return std_dev
data = np.array([7,5,4,9,12,45])
print("Standard Deviation of the sample is % s "% (stdev(data)))
print("Mean of the sample is % s " % (mean(data)))
To know more about the topic, visit the below links: -
https://brainly.in/question/15826005
https://brainly.in/question/48465904
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