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Answer:
The most realistic value for the standard deviation is 15.
Step-by-step explanation:
The standard deviation of a distribution is a measure of dispersion. It is a measure of the spread of the distribution from the mean of the distribution. It expresses how far most of the distribution is from the mean.
Mathematically, the standard deviation is given as the square root of variance. And variance is an average of the squared deviations from the mean.
Mathematically,
Standard deviation = σ = √[Σ(x - xbar)²/N]
x = each variable (ranges from 34 to 99)
xbar = mean = 78
N = number of variables
Now taking the given possible values of the standard deviation one at a time,
-14
The standard deviation cannot be negative as it is a square root of the average of the sum of square deviations from the mean. Since the square of a number cannot be negative, it directly translates that the standard deviation cannot be negative.
3
A small standard deviation like 3 indicates that the distribution mostly centres about the mean, with very little variation. And the distribution given has a mean (78) that is very far away from at least one of the variables in the distribution. Hence, 3 is too low to pass ad the standard deviation of this distribution described.
0
A standard deviation of 0 indicates that all the variables in the distribution have the same value as the mean. That is, the distribution only contains 1 number, probably multiple times. So, this cannot be the standard deviation for the distribution described.
56
This value represents a value that is too high to express the spread of the distribution described. The mean (78) is very close to the maximum value of the distribution, and far away from the lower value(s), indicating that most of the distribution is in and around the upper values with a few variables closer to the lower limit. A standard deviation as high as 56 for a mean of 78 translates to a distribution with most of variables far from the mean, which isn't the case here.
Moreso, a simple add of the standard deviation to the mean or subtracting the standard deviation from the mean should give at least one of the results with values within the distribution.
(Mean) + (Standard deviation) = 78 + 56 = 134 >> 99 (outside distribution)
(Mean) + (Standard deviation) = 78 - 56 = 22 << 34 (also outside the distribution)
15
This is the most realistic value for the standard deviation as it represents what the distribution described above is.
The mean (78) being close to the maximum value of the distribution, and far away from the lower value(s) indicates that most of the distribution is in and around the upper values with a few variables closer to the lower limit.
So, 15 indicates a perfect blend of small deviations due to the high values close to the mean and the very high deviation from the evidently few lower values.
(Mean) + (Standard deviation) = 78 + 15 = 93 < 99 (within distribution)
(Mean) + (Standard deviation) = 78 - 15 = 63 > 34 (also within the distribution)
Hope this Helps!!!
When The most realistic value for the standard deviation is 15.
Step-by-step explanation:
Standard deviation
- The standard deviation of a distribution is a measure of dispersion. also, It is a measure of the spread of the distribution from the mean of the distribution.
- when It expresses how far most of the distribution is from the mean.
- Then according to Mathematically, the standard deviation is given as the square root of variance.
- And also variance is an average of the squared deviations from the mean.
mathematically,
- When Standard deviation is = σ = √[Σ(x - xbar)²/N]
- After that x = each variable (ranges from 34 to 99)
- then xbar is = mean = 78
- Now N is = number of variables
- Then we take the given possible values of the standard deviation one at a time,
- -14 after that The standard deviation cannot be negative as it is a square root of the average of the sum of square deviations from the mean.
- Since the square of a number cannot be negative, also it directly translates that the standard deviation cannot be negative.
- After that 3 no when A small standard deviation like 3 indicates that the distribution mostly centers about the mean, with very little variation.
- And also the distribution given has a mean (78) that is very far away from at least one of the variables in the distribution.
- Hence proof that is, 3 is too low to pass ad the standard deviation of this distribution described.
- Then 0 when A standard deviation of 0 indicates that all the variables in the distribution have the same value as the mean.
- That means is, the distribution only contains 1 number, probably multiple times.
- So that, this can't be the standard deviation for the distribution described.
- Now 56 This value represents a value that is too high to express the spread of the distribution described.
- when The mean (78) is very close to the maximum value of the distribution, and also far away from the lower value(s), indicating that most of the distribution is in and also around the upper values with a few variables closer to the lower limit.
- when A standard deviation as high as 56 for a mean of 78 translates to a distribution with most of the variables far from the mean, which isn't the case here.
- More so, when a simple addition of the standard deviation to the mean or subtracting the standard deviation from the mean should have given at least one of the results with values within the distribution.
- After that (Mean) + (Standard deviation) = 78 + 56 = 134 >> 99 (outside distribution)
- Then (Mean) + (Standard deviation) = 78 - 56 = 22 << 34 (also outside the distribution)
- Now last digit 15 This is the most realistic and also a value for the standard deviation as it represents what the distribution described above is.
- When The mean (78) is close to the maximum value of the distribution, and also far away from the lower value(s) indicates that most of the distribution is in and also that around the upper values with a few variables closer to the lower limit.
- So that, 15 indicates a perfect blend of small deviations due to the high values close to the mean and also the very high deviation from the evidently few lower values.
- Then (Mean) + (Standard deviation) = 78 + 15 = 93 < 99 (within distribution)
- After that (Mean) + (Standard deviation) =
- Thus, 78 - 15 = 63 > 34 (also within the distribution)
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