Some sample questions

Topic : Descriptive statistics

1.a) An article describes an experiment to test the yield strength of circular tubes with caps welded to the ends. The first 18 yields (in kN) are:

96, 96, 102, 102, 102, 104, 104, 108, 126,126, 128, 128, 140, 156, 160, 160, 164,170

Construct a frequency distribution. Also plot a frequency histogram of yields. Is the distribution of yields symmetric?

1.b) The ten measurements that follow are furnace temperatures recorded on successive batches in a semiconductor manufacturing process (units are °F):

  944, 945, 950, 950, 951, 954, 955, 955, 956, 957

Construct a simple boxplot. Are the temperatures high most of the time?

1.c) The prices (in USD) of a gallon of regular gas at 12 gas stations somewhere on earth were

3.19, 3.09, 3.09, 2.93, 2.95, 3.09, 2.99, 2.99, 2.95, 2.99, 2.99, 2.97

  1. Calculate the sample mean and sample standard deviation of gasoline price.

  2. Construct a simple box-plot of gasoline price. Comment about the shape characteristics of the gasoline price distribution. Was the price of gasoline low most of the time?

1.d) Consider following camparative boxplot:

  1. Which month shows the highest and the lowest temperature respectively?
  2. Which has the highest median temperature?
  3. Which month shows greater variation in terms of IQR?

1.e) The “cold start ignition time” of an automobile engine is being investigated by a gasoline manufacturer. The following times (in seconds) were obtained for a test vehicle:

  1.75, 1.92, 2.62, 2.35, 3.09, 3.15, 2.53, 1.91

Compute sample mean, standard deviation and coefficient of variation of ignition time.

1.f) A certain brand of automobile tire has a mean life span of 35,000 miles, with a standard deviation of 2250 miles. The life spans of three randomly selected tires are 34,000 miles, 37,000 miles, and 30,000 miles. Find the z-score that corresponds to each life span. Determine whether any of these life spans are unusual.

1.g) The shear strengths of 20 spot welds in a titanium alloy are as follows:

5408    5431    5475    5442    5376    5388    5459    5422    5416    5435
5420    5429    5401    5446    5487    5416    5382    5357    5388    5457

Construct a frequency histogram of shear strengths data. Conclude whether the shear strength is approximately symmetric or not.

1.h) The following sample data presents the thickness (Å) of a metal layer on 20 silicon wafers resulting from a chemical vapor deposition (CVD) process. Scientists believe that the thickness is usually normally distributed having a bell-shaped distribution/symmetric for a smooth process. Construct a frequency histogram of metal thickness data. Conclude whether the process is smooth or not.

468,    459,    450,    453,    473,    454,    458,    438,    447,    463,
445,    466,    456,    434,    471,    437,    459,    445,    454,    423

1. i) Following fabric strengths were measured from an experiment:

1.3,    1.6,    0.5,    1.2,    1.1,    5.7,    0.6,    1.5,    1.3,    6.9.

Check whether there is/are any outlier/ outliers using 1.5*IQR rule.