91影视

The Minitab output is provided that include the following:

Sample size, \(N = 153\)

Sample mean, \(\bar x = 135.39\)

Sample median, \(\tilde x = 135.40\)

Trimmed mean, \({\bar x_{Tr}} = 135.41\)

Standard deviation, \(s = 4.59\)

SE mean = 0.37

Minimum, min = 122.20

Maximum, max = 147.70

Lower fourth, \({Q_1} = 132.95\)

Upper fourth, \({Q_3} = 138.25\)

From the Minitab output, the values of sample mean, sample median and trimmed mean are approximately identical to each other.The data's minimum and maximum values are found to be evenly spaced from the median of the data. This shows the good amount of symmetry present in the given data. The standard deviation is low which tells that the data values are close to the mean of the data and less variability.

This provides additional support to the fact that the data distribution is symmetrical.

Following are the steps to make boxplot by hand:

1. Draw a plot line of range 120 to 150.
2. Draw three vertical lines that consists of first quartile, second quartile and third quartile and make two horizontal lines to make it in rectangular form like a box for strength.
3. Draw whiskers on both sides of four boxplots and set the minimum and maximum value with respect to the obtained lower fence and upper fence.

The left whisker of the boxplot is slightly bigger than the right whisker indicate that, it is slightly right-skewed. Since, there are three outliers exist so the observations are distant from rest of the data. These outliers are minimum observation 122.20, and two maximum observations 147.7 and 147.7.