Basic Statistics · Unit 4
Measures of Central Tendency and Dispersion
Exam-focused notes for Measures of Central Tendency and Dispersion (Basic Statistics, STA154): what the TU syllabus asks and how it has actually been tested, with 6 solved past questions from this unit.
What this unit covers
- Mean, median, and mode
- Choice of appropriate central tendency measure
- Range and interquartile range
- Variance and standard deviation
- Coefficient of variation
- Methods of measuring dispersion
- Comparison of consistency between datasets
Comparison of consistency between datasets
Build System Consistency Analysis
A software development team is tracking the build sizes (in MB) produced by two different automated build systems during nightly integrations over 10 days. Which build system is more consistent? Justify your answer.
$$\begin{array}{|c|cccccccccc|}\hline \text{Build System A} & 88 & 92 & 94 & 85 & 90 & 95 & 89 & 87 & 91 & 86 \ \hline \text{Build System B} & 130 & 135 & 132 & 140 & 128 & 133 & 137 & 131 & 129 & 138 \ \hline \end{array}$$
[10]
Build System A (MB): 88, 92, 94, 85, 90, 95, 89, 87, 91, 86 Build System B (MB): 130, 135, 132, 140, 128, 133, 137, 131, 129, 138 $n = 10$ for each Since the two data sets have different means (different units/scale of build sizes), the correct measure of r...
Full solved answer →Response Time Consistency Comparison
A cloud service provider is evaluating the response times of two different server clusters over 10 requests. The company wants to compare the variability in response times between the two clusters. Here are the response times (in milliseconds) for the two clusters. Which cluster has more consistent response times?
$$\begin{array}{|c|cccccccccc|}\hline \text{Cluster A} & 88 & 92 & 94 & 85 & 90 & 95 & 89 & 87 & 91 & 86 \ \hline \text{Cluster B} & 130 & 135 & 132 & 140 & 128 & 133 & 137 & 131 & 129 & 138 \ \hline \end{array}$$
[10]
Cluster A (ms): 88, 92, 94, 85, 90, 95, 89, 87, 91, 86 (n = 10) Cluster B (ms): 130, 135, 132, 140, 128, 133, 137, 131, 129, 138 (n = 10) Since the two clusters have very different means, the correct measure to compare consistency is the Coefficient of Vari...
Full solved answer →Measuring Dispersion and Student Performance Analysis
Dispersion measures the scatter or spread of data about a central value. Methods are classified as absolute (same units as data) and relative (unit-free ratios/percentages). Absolute measures: 1. Range = Largest value − Smallest value ($L - S$). Simplest bu...
Full solved answer →Measures of Central Tendency and Computer Consistency Analysis
Measure Suitable Situation ----------------------------- Mean Data is fairly symmetric with no extreme outliers; all values must be used; further algebraic/statistical treatment (like SD, CV) is needed; quantitative data. Median Distribution is skewed or ha...
Full solved answer →Cyber Cafe Download Time Analysis
There are two popular Cyber Cafes (namely Cafe A and Cafe B) in Kathmandu located at Thamel area. Each of them has good number of computers in the cyber and maintains peace, comfort and good working environment. Each customer, before entering into the cafe, asks to the cafe owner about the average time to download an image file since the internet in Kathmandu is a bit of sporadic. Each of them replied that the time to download an image file is on an average no more than 70 seconds. The following is the data of downloading time for an image file experienced by 8 customers in each cafe in some random 8 different days.
$$\begin{array}{|c|c|}\hline \text{Cafe A (in sec)} & \text{Cafe B (in sec)} \ \hline 70 & 70 \ 55 & 75 \ 55 & 72 \ 45 & 73 \ 40 & 73 \ 80 & 80 \ 75 & 74 \ 69 & 40 \ \hline \end{array}$$
a.) Explain whether the owner's response to the customers are satisfied in each cafe? Even having the average waiting time within the owner's limit, is there any further comments on the data with reference to measures of central tendency you have computed? Discuss. [3]
b.) What similarities and differences are observed based on the average download time in Cafe A and in Cafe B? [2]
c.) Compare the download time between two cafes with respect to variability and shape of the data distribution. [2.5]
d.) On the basis of your statistical analysis, which cafe would be suggested to the customers so that one can download an image file in a lesser time? [2.5]
Cafe A (sec) Cafe B (sec) ------ 70 70 55 75 55 72 45 73 40 73 80 80 75 74 69 40 - Sample size each: $n = 8$ - Owner's claimed limit: average download time $\leq 70$ sec --- Mean: Cafe A: $\bar{x}A = \dfrac{70+55+55+45+40+80+75+69}{8} = \dfrac{489}{8} = 61....
Full solved answer →Coefficient of variation
What is the difference between relative and absolute statistical measure? J.J. Thomson discovered the electron by isolating negatively charged particles for which he could measure the mass-charge ratio. This ratio appeared to be constant over a wide range of experimental conditions and, consequently, could be characteristics of new particles. His observations from two different cathode-ray tubes that used air as the gas. Which tube is more homogeneous?
$$\begin{array}{|c|c|c|c|c|c|c|c|}\hline \text{Tube I} & 0.57 & 0.34 & 0.43 & 0.32 & 0.48 & 0.40 & 0.40 \ \hline \text{Tube II} & 0.53 & 0.47 & 0.47 & 0.51 & 0.63 & 0.61 & 0.48 \ \hline \end{array}$$
[10]
Absolute measures of dispersion: - Expressed in the same units as the original data - Examples: Range, Quartile Deviation, Mean Deviation, Standard Deviation - Measure scatter in absolute terms - Cannot compare variability between series with different unit...
Full solved answer →Make Unit 4 stick
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