In: Math
84, 67, 85, 82, 99, 78, 88, 94, 82, 90, 97, 88, 93, 91, 94, 80, 81, 86, 95, 91, 88, 96, 75, 90, 85, 89, 95, 85, 85, 86, 91.
A) Make a relative frequency histogram of the data using 7 classes.
B)According to Chebyshev, for the given data, between what two values could you expect to find 75% of the data?
Solution:
To find the relative frequency distribution, we first need to find the class width. We know that the range of the given data is 99 - 67 = 32 and the number of classes = 7. Therefore, the class width is:
Therefore, the relative frequency distribution and relative frequency histogram is:
B)According to Chebyshev, for the given data, between what two values could you expect to find 75% of the data?
Answer: The mean and standard deviation of the given data is:
According to Chebyshev's theorem, 75% of data lies within two standard deviations of the mean. Therefore, we have:
According to Chebyshev, for the given data, between 73.6 and 101.3 we would expect to find 75% of the data