This Statistics Test is about MCQs Basic Statistics Quiz with Answers. There are 20 multiple-choice questions from Basics of Statistics, measures of central tendency, measures of dispersion, Measures of Position, and Distribution of Data. Let us start with the MCQS Basic Statistics Quiz with Answers
Online Multiple-Choice Questions about Basic Statistics with Answers
Online MCQs Basic Statistics Quiz
If any value in the data is negative, it is not possible to calculate
Mode of the values 2, 6, 8, 6, 12, 15, 18, and 8 is
Mode of the values 3, 5, 8, 10, and 12 is
The first step in computing the median is
If $x=3$ then which of the following is the minimum
The dispersion expressed in the form of a ratio or coefficient and independent from units of measurement is called
The half of the difference between the third and first quartiles is called
The difference between the largest and smallest value in the data is called
The most important measure of dispersion is
Which of the following is a relative measure of dispersion
Which of the following is an absolute measure of dispersion
If 6 is multiple t all observations in the data, the mean is multiplied by
Which of the properties of Average Deviation considers Mathematics assumption wrong?
What would be the changes in the standard deviation if different values are increased by a constant?
Two sets of distribution are as follows. For both of the sets, the Range is the same. Which of the demerits of Range is shown here in these sets of distribution? Distribution 1: 30 14 18 25 12 Distribution 2: 30 7 19 27 12
For a set of distributions if the value of the mean is 20 and the mode is 14 then what is the value of the median for a set of distributions?
Who used the term Statistics for the first time?
The median is larger than the arithmetic mean when
Fill in the missing words to the quote: “Statistical methods may be described as methods for drawing conclusions about —————- based on ————– computed from the —————“.
In general, which of the following statements is FALSE?
This post is about the MCQs Basic Statistics Quiz with Answers. There are 20 multiple-choice questions about the Basics of Statistics, covering measures of central tendency (Mean, Median, Mode, Geometric Mean, and Harmonic Mean), Measures of Dispersion, Deviations, Relationships between different measures of central tendency, Coding Methods for computing Mean, etc. Let us start with the MCQs Basic Statistics Quiz.
Quartile deviation denoted by QD is the absolute measure of dispersion and it is defined as the half of the difference between the upper quartile ($Q_3$) and the lower quartile ($Q_1$).
Table of Contents
The Quartile Deviation also known as semi-interquartile range (Semi IQR), is a measure of dispersion that focuses on the middle 50% of the data. It is calculated as half the difference between the Third Quartile ($Q_3$) and the First Quartile ($Q_1$). One can write it mathematically as
$$QD = \frac{Q_3-Q_1}{2}$$
Note that the interquartile range is only the difference between the upper quartile ($Q_3$) and the lower quartile ($Q_1$), that is,
$$Interquartile\,\, Range = IRQ = Q_3 – Q_1$$
The Relative Measure of Quartile Deviation is the Coefficient of Quartile Deviation and is given as
When dealing with skewed data or data with outliers.
When a quick and easy measure of dispersion is needed.
Interpretation QD
Spread: A larger quartile deviation indicates greater variability in the middle portion of the data. Outliers: QD is less sensitive to extreme values (outliers) compared to the standard deviation.
Quartile Deviation for Ungrouped Data
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The above data is already sorted and there are a total of 96 observations. The first and third quartiles of the data can be computed as follows:
$Q_1 = \left(\frac{n}{4}\right)th$ value $= \left(\frac{96}{4}\right)th$ value $= 24th$ value. The 24th observation is 59, therefore, $Q_1=59$.
$Q_3 = \left(\frac{3n}{4}\right)th$ value $= \left(\frac{3\times 96}{4}\right)th$ value $= 72th$ value. The 72nd observation is 108, therefore, $Q_3=108$.
Less affected by outliers: Makes it suitable for skewed data.
Easy to calculate: Relatively simple compared to standard deviation.
Disadvantages of QD
Ignores extreme values: This may not provide a complete picture of the data’s spread.
Less sensitive to changes in data: Compared to standard deviation.
In summary, Quartile deviation is a valuable and useful tool for understanding the spread of data, particularly when outliers are present. By focusing on the middle 50% of the data, it provides a robust measure of dispersion that is less sensitive to extreme values. However, it is important to consider its limitations, such as its insensitivity to outliers and changes in data.
Frequently Asked Questions about Quartile Deviation
What is quartile deviation?
What are the advantages of QD?
What are the disadvantages of QD?
What is IQR?
What is Semi-IQR?
How QD is interpreted?
How QD is computed for grouped and ungrouped data?
