Question

Analyze the data set of BMI:

23.8
23.2
24.6
26.2
23.5
24.5
21.5
31.4
26.4
22.7
27.8
28.1
25.2
23.3
31.9
33.1
33.2
26.7
26.6
19.9
27.1
23.4
27.0
21.6
30.9
28.3
25.5
24.6
23.8
27.4
28.7
26.2
26.4
32.1
19.6
20.7
26.3
26.9
25.6
24.2

Determine the measures of center for the data (mean, median, and mode) and explain which one describes the center of this data best.

Determine measures of variation (range, standard deviation, and variance) and explain which one describes the spread of this data best.

Determine the quartiles and the IQR (Inter Quartile Range).

Explain the method of determining outliers in the data and list any outliers.

Create the modified boxplot of the data showing any outliers.

Answer 1

Ca The step-by-step instructions to obtain Descriptive Statistics using Minitab18 * Store the data in to the Minitab worksheet * Stat -Basic Stati stics ->Display Des criptive Stati stics. * Click on mean, medi an and mode. *Click on Statistics * Click on ok The descriptive stati stics output

Descriptive Statistics: X Statistics N for Mode Mode 40 0 25.998 26.200 23.8, 24.6, 26.2, 26.4 2 Variable N N* Mean Median

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Explanation:

The median is the best of the measures of central tendency, it describes well about the data, while the mean is most affected by the outliers, the mode is the alternative measure of central tendency, when the data is skewed.

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Descriptive Statistics:X Statistics Variable N N* StDev Variance Range 40 0 3.43 11.770 13.600

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Explanation:

The best measure of spread is range as it is not much affected by outliers in the data. The standard deviation and variance are not good measures of the data.

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Interpretation:

The above boxplot enables that there exists no outliers in the data set. The method of determining outliers using the Inter quartile range. The lower bound and upper bound of the boxplot is First quartile - 1.5 times the iqr and the upper bound is the Third quartile+1.5 times IQR. If the data point is not within the range of the bounds of the boxplot, we may consider it as an outlier in the data.