Data Analysis
A study examined how long aircraft air conditioning units operated after being repaired. Here
are the operating times (in hours) for one unit:
32
51
58
63
65
69
90
97
98
100
103
106
117
118
118
120
124
128
129
132
150
152
185
196
225
231
289
a) Make a histogram of these data, using 40 hour wide classes, starting with 0<time < 40, 40
< time < 80,…..
b) Describe the overall shape of the distribution. Is it roughly symmetric, skewed to the right
, or skewed to the left? Are there any outliers?
c) Is the five number summary of the mean and standard deviation a better brief summary for this distribution? Explain your choice. Calculate the one of these summaries that you
choose.
I have given a site where you can find most of the information regarding general statements about confidence intervals. For the T test, Z test, etc. please show your calculations and someone will check them for you. By the way, this forum (and others like it on the Internet) simply cannot draw graphs, histograms, and the like. You can, however, find graphs and histograms that may be similar to your problem and compare your work to that which you find on the Internet.
a) To make a histogram of the data, we can group the data into classes of 40-hour wide intervals. The intervals would be as follows:
0 < time < 40, 40 < time < 80, 80 < time < 120, 120 < time < 160, 160 < time < 200, 200 < time < 240, 240 < time < 280, 280 < time < 320.
To construct the histogram, we count the frequency of data falling within each interval. This can be done using software like Excel or Google Sheets.
b) To describe the overall shape of the distribution, we need to look at the histogram. Based on the histogram, we can determine if the distribution is roughly symmetric, skewed to the right, or skewed to the left.
If the histogram is roughly symmetric, the data is evenly distributed around the center. If it is skewed to the right, the data is concentrated on the left side and has a longer tail on the right. If it is skewed to the left, the data is concentrated on the right side and has a longer tail on the left.
To identify outliers, we can look for values that are significantly different from the majority of the data points. These are usually data points that are much higher or lower than the rest.
c) The choice between a five number summary, mean, and standard deviation as a better brief summary for this distribution depends on the distribution's shape and presence of outliers.
If the distribution is roughly symmetric and there are no outliers, then the mean and standard deviation can provide a good summary. The mean represents the average value of the data, while the standard deviation measures the spread or variability of the data around the mean.
However, if the distribution is skewed or there are outliers present, the five number summary (minimum, quartiles Q1, Q2, Q3, and maximum) would be a better summary. The five number summary provides information about the median, lower and upper quartiles, minimum, and maximum values. It is robust to outliers and can represent the central tendency and spread of the data more accurately.
To calculate the mean and standard deviation, you can use a statistical software like Excel or Google Sheets.