The two sets of observations are given below : Set I Set II –
x = 82.5 –
x = 48.75 = 7.3 = 8.35 Which of two sets is more consistent ?
Answers
Answer:
48.75 is more consistent
The set I is more consistent than set II
To Find:
- Which of two sets is more consistent
Given:
- Set I: x = 82.5, σ = 7.3
- Set II: x = 48.75, σ = 8.35
Solution:
Standard deviation (σ) is a measure of how spread out the data is in a set of observations. It is calculated by finding the difference between each data point and the mean (average) of the data set, squaring each difference, adding these squares, and then taking the square root of the sum of the squares.
A smaller standard deviation indicates that the data is more tightly grouped around the mean, which means it is more consistent. In other words, if the data points are close to the mean, the standard deviation will be small, and if the data points are spread out, the standard deviation will be large.
In set I, the mean is 82.5 and the standard deviation is 7.3, this means that most of the data points are within 7.3 units of the mean (82.5).
In set II, the mean is 48.75 and the standard deviation is 8.35, this means that most of the data points are within 8.35 units of the mean (48.75).
Therefore, set I is more consistent as the data points are more tightly grouped around the mean and the standard deviation is smaller compared to set II.
Alternatively, the coefficient of variation (CV) is another way to measure the consistency of data, it is the ratio of the standard deviation to the mean, multiplied by 100. The lower the CV, the more consistent the data is. The CV for set I is 8.8% and for set II is 17.1%, this also confirms that set I is more consistent than set II.
Therefore,The set I is more consistent than set II
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