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Download the attached data file. Use the data file to answer the questions 1 to 5 1. Select a proper variable and use a bar graph to describe the distributions of this variable (show percentage, increasingly) a. Use a paragraph to describe the frequency distribution and relative frequency of this variable. Indicate the mode 2. Construct two pie charts by using another proper variable by further dividing this variable into two categories with another two-leveled variable a. Also, use a paragraph to describe the frequency distribution and relative frequency of the first variable by the second variable 3. Select a proper variable and use a histogram to show the distribution of this variable a. Use a paragraph to describe the following statistics: Mean, Standard Deviation (as a sample), 5-number summary (min, Q1, median, Q3, and Max) b. Also, use a box plot to identify the possible outliers. Compute the upper and lower boundaries (limits) of the dataset. 4 Select another proper variable and use a Stem-and-Leaf plot to show the distribution of this variable a. Use a paragraph to describe the following statistics: Mean, Standard Deviation (as a sample), 5-number summary (min, Q1, median, Q3, and Max) b. Also, use a box plot to identify the possible outliers. Compute the upper and lower boundaries (limits) of the dataset. 5. Check if any of the variables is normally distributed. Recheck the normality after the outliers were removed

G H 1 Female? Hair LibraryBirth Class Level 2 FALSE Brown TRUE First Sophomore 3 FALSE Brown TRUE First Sophomore 4 FALSE Blond FALSE Second Senior or higher Difficult IQ Temp HeightWeight Credit 395 205 180 130 130 163 175 180 180 190 190 3 144 69 72 130 70 3 100 70 2115 72 10 TRUE |Brown FALSE |First Senior or higher 6 TRUE Brown FALSE Second Freshman 7 FALSE Brown TRUE Third Sophomore 8 FALSE IBrown FALSE First Junior 9 FALSE BlackTRUE First Senior or higher 10 FALSE Brown FALSE First Junior 11 FALSE Brown TRUE First Senior or higher 71 12 12 12 90 72 385 2 12567 3 150 67 3 105 395 3 115 41 1001 80 2 115 3 127 4 85 4 115 3 100 72 4 85 72 75 12 б5 12 TRUE Brown FALSE Second Sophomore 12 13 FALSEBlack FALSE Other Senior or higher 14 FALSE Brown TRUE Third Sophomore 15 FALSE Brown FALSE SecondJunior 16 FALSE Brown TRUE First Sophomore 17 FALSE BlackTRUE Third Sophomore 18 FALSE 19 FALSE Blond FALSE Second Sophomore 20 FALSE Brown TRUE Third Junior 23 72 12 12 12 13 13 13 13 72 225 72 165 175 180 TRUE First Senior or higher 71 73

math   Statistics-And-Probability   
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Answer #1

1a. We consider the variable Female? and call it Sex.

Barplot of Sex (O if Male; 1 otherwise) 90 80 70 60 50 40- 30 20 10- 0- Sex Percent is calculated within all data.Out of 19 observations 16 are Male and three are females. Relative frequencies are 84.21% for the males and 15.79% for the females. Naturally Modal value is the Males, which has the highest frequency.

3a. We consider the variable Height, which is a continuous variable, The relevant statistics are

Mean StDev Minimum Q1 Median Q3 Maximum
68.32 9.82 30.00 67.00 71.00 72.00 77.00

3b. The boxplot is given below

Boxplot of Height 80- 70 60 50 40 30The boxplot shows one outlier, which by inspection is 30.

5. We plot the histogram with and without outlier to check normality.

Histogram of Height (with outlier) 12- 10 喆 old 6. 一 4 2 30 40 50 60 70 The histogram shows departure from symmetry and hence non normality.

Histogram of Height(witout outlier) 9 8 6 2 68 70 72 74 76 78 C3This histogram is more or less symmetric with a single peak. Hence normality is adequate.

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