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Answer :
A high standard deviation indicates that the data points are spread out over a wider range of values, while a low standard deviation indicates that the data points are tightly clustered around the mean. It is commonly used in various fields such as finance, economics, engineering, and social sciences to analyze data and make informed decisions.
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The standard deviation is given as 35 seconds and the mean is given as 163 seconds.
Define the term standard deviation?
A statistical measure known as standard deviation can be used to quantify how variable or dispersed a set of data is. It gauges how far the values are from the data's mean (average).
sample mean = population mean
+ [population standard deviation / √(sample size)] × Z
where Z is the standard normal distribution variable corresponding to the desired level of probability.
Substituting the given values,
sample mean = 163 + (35 / √8 ) × 1.55 ≈ 180.54
So the sample mean length of 8 randomly selected songs is expected to be around 180.54 seconds.
To find the symmetric length values around the mean, we can use the formula:
Lower value = population mean - (sample mean - population mean)
= 2 × population mean - sample mean
Upper value = population mean + (sample mean - population mean)
= 2 × sample mean - population mean
Substituting the given values,
Lower value = 2 × 163 - 180.54 ≈ 145.46
Upper value = 2 × 180.54 - 163 ≈ 217.08
Therefore, there is a 88% probability that the sample mean length of 8 randomly selected songs is between 145.46 and 217.08 seconds, symmetric to the mean of 163 seconds.
The standard deviation is given as 35 seconds and the mean is given as 163 seconds.
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