Methods for describing sets of data

  

1. The Lamp data set (the sample was collected randomly) contains the lifetimes, in hours, of fifty 40-watt, 110-volt internally frosted incandescent lamps, taken from forced life tests. Use RStudio for all computations. The data set can be found in the excel file Lamp with a variable name Lifetimes. 

Source: Walpole, R.E., Myers, R.H., Myers, S.L., & Ye, K. (2012). Probability & Statistics for Engineers & Scientists. Boston, MA: Pearson.

a) Report sample mean and median of lifetimes. (total 4 points, 2 points each)

b) Report sample standard deviation and IQR (Interquartile range) of lifetimes. 

(total 4 points, 2 points each)

c) Report the mode of the lifetimes. Classify the distribution based on mode. (3+1 = 4 points)

d) Report a five-number summary of the lifetimes in the following table in the order (report one decimal place). (total 7.5 points, 0.5 point each box)

  

Name of   statistics

 

Value

 

Measurement   unit

e) Find and interpret the 90th percentile of the lifetimes on context. (2+2 = 4 points)

f) Produce a relative frequency histogram of the lifetimes. Label the axes properly. (3 points)

g) Construct a box plot of the lifetimes. (3 points)

h) Describe the distribution of lifetimes. Hint: Don’t forget your SOCS! (S – Stands for shape, O – stands for outlier, C – stands for center, and S – stands for spread) (8 points total, 2 points each)

i) Interpret the IQR (Interquartile range) of lifetimes on the context. (3 points)

2. The Rio data set includes the top 10 medal winning countries from the Rio 2016 Olympics and how many total medals they won. The data set can be found in the excel file Rio with a variable Medal. 

a) Use RStudio to create a frequency and relative frequency distribution of the variable Medal. Combine both of these distributions in a single table. (3 points)

b) Use RStudio to create a frequency bar graph of the medal data. Label the axes properly. (3 points)

c) Describe the distribution of top 10 medal winning countries from the Rio 2016 Olympics. (3.5 points)

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