ANSWER
The standard deviation is [tex]7.8[/tex] correct the nearest tenth.
EXPLANATION
The data set given to us is [tex]55,37,52,50,33,46,53[/tex].
The standard deviation of the given data set can be calculated using the formula,
[tex]Standard\:deviation=\sqrt{\frac{(x-\bar X)^2}{n} }[/tex]
where [tex]\bar X=\frac{\sum x}{n}[/tex]
[tex]\bar X=\frac{55+37+52+50+33+46+53}{7}[/tex]
[tex]\bar X=\frac{326}{7}[/tex]
[tex]\bar X=46.57[/tex]
We now find the standard deviation as follows;
[tex]SD=\sqrt{\frac{ (55-46.57)^2+(37-46.57)^2+(52-46.57)^2+(50-46.57)^2+(33-46.57)^2+(46-46.57)^2+(53-46.57)^2 }{7} }[/tex]
[tex]Standard\:deviation=\sqrt{\frac{71.06+91.58+29.48+11.76+184.14+0.32+41.34}{7} }[/tex]
[tex]Standard\:deviation=\sqrt{\frac{429.68}{7} }[/tex]
[tex]Standard\:deviation=\sqrt{61.38}[/tex]
[tex]Standard\:deviation=7.84[/tex]
Answer:
Standard deviation of the data set = 7.84
Step-by-step explanation:
To calculate the standard deviation of the data set first we take the mean of the data .
Mean = [tex]\frac{(55+37+52+50+33+46+53)}{7}[/tex]
= [tex]\frac{326}{7}[/tex]
= 46.57
Now we subtract the mean from data set and square the answer.
55 - 46.57 = 8.43² = 71.06
37 - 46.57 = -9.57² = 91.58
52 - 46.57 = 5.43² = 29.48
50 - 46.57 = 3.43² = 11.76
33 - 46.57 = -13.57² = 184.14
46 - 46.57 = -0.57² = 0.32
53 - 46.57 = 6.43² = 41.34
Then we will take the mean of squared result.
[tex]\frac{(71.06+91.58+29.48+11.76+184.14+0.32+41.34)}{7}[/tex]
= [tex]\frc{429.68}{7}[/tex]
Variance = 61.38775509
Lastly take the square root of variance
= [tex]\sqrt{61.38775509}[/tex]
= 7.835033828 rounded to 7.84
Standard deviation of the data set = 7.84
