Stat 202: Generate a Frequency Table for the Data Set - Statistics Assignment Help

Assignment Task:

Task:

1. The bar plot for a data set is provided below. Please use the information in the bar plot to answer parts (a), (b), (c) and (d): [1]

(a) Generate a frequency table for the data set shown in the bar plot. 2 [2]

(b) What is the mean of the data set shown in the bar plot? Show how the mean is calculated in this case. [2]

(c) What is the median of the data set shown in the bar plot? Explain how this value is determined (i.e. starting with the rank-ordered list of values).

(d) What is the mode of this data set?[1] 3 [2]

(e) The mode is often considered to be a measure of center, like the mean and the median, but for the data set in the provided barplot the mode is higher than the mean and median. Sketch a bar plot for a (different) data set where the mean, median and mode would all take very similar values. 4 [7]

2. The next two questions will ask you to draw and describe box plots. For these box plots, please do not make any attempt to identify outliers or to plot outliers separately (i.e. have the box plot be a visualization of the five number summary for the data set). [2]

(a) Draw a box plot for a data set that shows skewness to the right. Explain generally what it means for a data set to be skewed to the right, and briefly describe how you selected values for the five number summary to depict skewness to the right. [1]

(b) Where, roughly, would you expect the mean to be located on the boxplot you drew in part (a)? 5 [2]

(c) Draw a box plot for a data set where the median is 10, the inter-quartile range is 4, and whose histogram would be symmetrical and approximately bell-shaped. [2]

(d) Suppose every data value in the data set from part (c) was duplicated (i.e. if the original data set was the three numbers 1, 4, 7, after duplication the set would be the six numbers 1, 1, 4, 4, 7,

7). How would you expect the shape of your boxplot to change? Justify your answer with reference to the definitions of the values included in the five-number summary. 6 [8]

3. As part of a game at a birthday party, a fair, six-sided die is rolled. How the game proceeds depends on the outcome of the die roll as follows: If the outcome is 1, 2, or 3: The player is rewarded with a piece of candy. If the outcome is 4 or 5: The player is rewarded with a sticker. If the outcome is 6: The player is rewarded with both a sticker and a piece of candy. Let the following events be defined by the symbols A, B, C: A : The player’s reward includes a sticker. B : The player rolls a 4. C : The player’s reward includes a piece of candy. (a) What is P(A)?

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