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anita010963
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a distribution has a mean of 260 and a standard deviation of 18 What is the percentage of data values that will fall in the range of 215 to 305 please simple or explain
Determining the percent of data values in a specific range can help to identify patterns and trends in the data, and can also provide information on the distribution of the data.
Chebyshev's Theorem is a statistical theorem that provides a lower bound for the proportion of data values that fall within a certain number of standard deviations from the mean. It can be used to determine the minimum percentage of data values that will fall within a specific range, such as the 215-305 range.
To calculate the percent of data values in a specific range using Chebyshev's Theorem, you first need to calculate the mean and standard deviation of the data. Then, you can use the formula: 1 - (1/k^2), where k is the number of standard deviations from the mean that define the range. For the 215-305 range, k would be (305-215)/standard deviation.
Yes, there are some limitations to using Chebyshev's Theorem. It assumes that the data is normally distributed, so if the data is heavily skewed or has outliers, the theorem may not provide an accurate estimate of the percentage of data values in a specific range.
Other methods that can be used to determine the percent of data values in a specific range include calculating the z-score and using the empirical rule. These methods also require the data to be normally distributed, but may provide more accurate estimates than Chebyshev's Theorem in certain situations.