Intro level Statistics exam

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Intro level Statistics exam

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Name __________________________ AET 4843 Midterm Spring 2017 You must show your work in a logical flow to receive full and partial credit. Partial credit cannot be give if work is not clearly shown. 1. Using the numbers from Data Table 1, determine the mean, median, and mode: Mean ________________, Median __________________, Mode ___________________ # 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Table 1 Value 44 46 49 55 47 49 52 51 50 47 39 55 61 48 55 2. Draw a histogram using the numbers from Table 1. Use 3 cells and label the cell midpoints with the value. (Use the axes below.) 3. A sampling of the number of times per week that Slaven trips up the stairs is taken over the year. The following frequencies are observed per week (number of occasions per week: frequency of observations): 0:12, 1:18, 2:29, 3: 38, 4:45, 5:30. Find the mean. 4. Use only the values of Data Table 1. What is the sample standard deviation? AND, what is the coefficient of variation of these numbers? 5. A process is known to have a normal distribution, μ = 216.4, & σ = 5.92. A customer says that no less than 98% of a shipment can be below the upper specification limit. What is that limit? 6. A process is known to have a normal distribution and σ = 12.8. If the facility has a goal to have no more than 1% below the specification limit of 564.3, then where does the process average need to be set? 7. Use Data Table 2 to create an X-bar and R chart. Determine the UCL and LCL of each of these charts. Indicate any that are out of control (assume assignable cause) and determine a revised UCL and LCL. Show your work, but place your final answers in the table below. n = 8. X-double bar R-bar UCLx-bar LCLx-bar UCLR LCLR # 1 2 3 4 5 6 7 8 9 10 11 Table 2 x-bar 68.5 67.6 69.1 68.0 67.5 68.9 73.9 68.7 67.9 68.1 68.1 R 1.4 1.3 1.8 1.7 0.9 1.1 1.3 0.7 1.5 0.8 0.5
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Explanation & Answer

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Using the numbers from Data Table 1, determine the mean, median, and mode:
Table 1
Value
44
46
49
55
47
49
52
51
50
47
39
55
61
48
55

𝑀𝑒𝑎𝑛 =

∑𝑛
𝑖=1 𝑥𝑖
𝑛

=

44+46+49+55+47+49+52+51+50+47+39+55+61+48+55
15

𝑀𝑒𝑎𝑛 = 49.867

Given the set of values: [44, 46, 49, 55, 47, 49, 52, 51, 50, 47, 39, 55, 61, 48, 55]
The median is the value separating the higher half of a data sample, from the lower half.

Median = 51

If we order the set from the low...


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