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Below are the lifetimes, in hours, of fifty 40-watt, 110-watt internally frosted incandescentlamps, taken from forced life tests:919 1196 785 1126 936 9181156 920 948 1067 1092 11621170 929 950 905 972 10351045 855 1195 1195 1340 1122938 970 1237 956 1102 1157978 832 1009 1157 1151 1009765 958 902 1022 1333 8111217 1085 896 958 1311 1037702 923Construct :a) Skeletal box plot

Question

Below are the lifetimes, in hours, of fifty 40-watt, 110-watt internally frosted incandescentlamps, taken from forced life tests:919 1196 785 1126 936 9181156 920 948 1067 1092 11621170 929 950 905 972 10351045 855 1195 1195 1340 1122938 970 1237 956 1102 1157978 832 1009 1157 1151 1009765 958 902 1022 1333 8111217 1085 896 958 1311 1037702 923Construct :a) Skeletal box plot

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Solution

I'm sorry, but as a text-based AI, I'm unable to create graphical representations such as a skeletal box plot. However, I can guide you on how to create one.

  1. Arrange the data in ascending order: 702, 765, 785, 811, 832, 855, 896, 902, 905, 918, 919, 920, 923, 929, 936, 938, 948, 950, 956, 958, 958, 970, 972, 978, 1009, 1022, 1035, 1037, 1045, 1067, 1085, 1092, 1102, 1122, 1126, 1151, 1156, 1157, 1162, 1170, 1195, 1195, 1196, 1217, 1237, 1311, 1333, 1340.

  2. Find the median (Q2), which is the middle value. If there is an even number of observations, the median will be the average of the two middle numbers. In this case, the median is (1022+1035)/2 = 1028.5

  3. Find the lower quartile (Q1), which is the median of the lower half of the data (not including Q2 if your number of observations is odd). In this case, Q1 is (918+920)/2 = 919.

  4. Find the upper quartile (Q3), which is the median of the upper half of the data (not including Q2 if your number of observations is odd). In this case, Q3 is (1162+1170)/2 = 1166.

  5. The interquartile range (IQR) is Q3 - Q1 = 1166 - 919 = 247.

  6. Any data point less than Q1 - 1.5IQR or greater than Q3 + 1.5IQR is considered an outlier. In this case, there are no outliers.

  7. Now, you can draw a box from Q1 to Q3 with a line inside the box at Q2. This is your box plot. The "whiskers" of the plot extend from the box out to the smallest and largest observations that are not outliers.

Remember, this is a skeletal box plot, so it does not include outliers or mean.

This problem has been solved

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