A population has m = 50. What value of s would make X = 55 a central, representative score in the population?
s=20
To determine the value of s that would make X = 55 a central, representative score in the population, we need to consider the concept of standard deviation.
In statistics, the standard deviation (s) represents the measure of variability or spread of a population's values around the mean (X). It indicates how much the individual scores typically deviate from the average.
To make X = 55 a central, representative score, we need to ensure that it falls in the center of the population distribution. In other words, the distance or deviation between X = 55 and the mean (X̄) should be minimal.
Given that the population mean is X̄ = m = 50, we can calculate the standard deviation (s) using the formula:
s = | X - X̄ |
Plugging in the values, we have:
s = | 55 - 50 |
s = | 5 |
Therefore, the value of s that would make X = 55 a central, representative score in the population is s = 5.
To determine the value of s that would make X = 55 a central, representative score in the population, we need to understand the concept of standard deviation and how it relates to the mean.
The standard deviation (s) measures the spread or variability of a data set. It tells us how far, on average, each data point in the set is from the mean. A smaller standard deviation indicates that the data points are closer to the mean, while a larger standard deviation means the data points are more spread out.
To find s, we can use the formula for standard deviation, which is the square root of the variance. The variance, in turn, is calculated by finding the average of the squared differences between each data point and the mean.
In this case, we're given the population mean (m) as 50 and the desired score (X) as 55. Since we want X = 55 to be a central, representative score, it means that the mean (m) and X should be equal.
To find s, we can set up the equation as follows:
X = m + s
Substituting in the given values:
55 = 50 + s
Now, we can solve for s:
s = 55 - 50
s = 5
Therefore, to make X = 55 a central, representative score in the population with a mean of 50, the value of s (standard deviation) should be 5.
Assuming a normal distribution, if the mean (m) = 50, no value of standard deviation (s) would make 55 a measure of central tendency.
If the distribution is skewed, s has no definite meaning. However, the mode or median could be 55.