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This quiz contains MCQs about Basic Statistics with answers covering variable and type of variable, Measures of central tendency such as mean, median, mode, Weighted mean, data and type of data, sources of data, Measures of Dispersion/ Variation, Standard Deviation, Variance, Range, etc. Let us start the MCQs Basic Statistics Quiz.
Basic statistics deals with the measure of central tendencies (such as mean, median, mode, weighted mean, geometric mean, and Harmonic mean) and measure of dispersion (such as range, standard deviation, and variances). Basic statistical methods include planning and designing the study, collecting data, arranging, and numerical and graphically summarizing the collected data. Basic statistics also used to perform statistical analysis to draw meaningful inferences.  A basic visual inspection of data using some graphical and numerical statistics may give some useful hidden information already available in the data. The graphical representation includes a bar chart, pie chart, dot chart, box plot, etc. Companies related to finance, communication, manufacturing, charity organizations, government institutes, simple to large businesses, etc. are all examples that have a massive interest in collecting data and measuring different sorts of statistical findings. This helps them to learn from the past, noticing the trends, and planning for the future.
Concept:
Calculation: We are already having the cumulative frequencies. Let's find out the frequencies:
Hence, the frequency of class intervals 30,000 - 40,000 is 6.
Concept: Cumulative frequency is the sum of all the previous frequencies up to the current point. The cumulative frequency is calculated by adding each frequency from a frequency distribution table to the sum of its predecessors. The last value will always be equal to the total for all observations since all frequencies will already have been added to the previous total. Also, Frequency of any class = cumulative frequency of class - cumulative frequency of preceding class Calculation: Let's calculate the frequency of each class using the cumulative frequencies of each class:
Clearly, we can see that 39 - 41 has the maximum frequency i.e.,13. Hence, 39 - 41 has the maximum frequency. India’s #1 Learning Platform Start Complete Exam Preparation
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A graph of a cumulative frequency distribution is called Ogive. Ogive: In statistics, an ogive, also known as a cumulative frequency polygon, can refer to one of two things:
The points plotted as part of an ogive are the upper-class limit and the corresponding cumulative absolute frequency or cumulative relative frequency. The ogive for the normal distribution resembles one side of an Arabesque or ogival arch, which is likely the origin of its name. 1. Frequency Polygon: A frequency polygon is a graph constructed by using lines to join the midpoints of each interval or bin. The heights of the points represent the frequencies. A frequency polygon can be created from the histogram or by calculating the midpoints of the bins from the frequency distribution table. 2. Frequency Curve: A Frequency Curve is a smooth curve which corresponds to the limiting case of a histogram computed for a frequency distribution of a continuous distribution as the number of data points becomes very large. 3. Pie Diagram: A pie diagram is a circular statistical graphic, which is divided into slices to illustrate numerical proportion. In a pie chart, the arc length of each slice is proportional to the quantity it represents. Thus, option 1 is the correct answer. India’s #1 Learning Platform Start Complete Exam Preparation
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Calculation Let assume the class interval and frequency table for this histogram to solve this question
Histogram for this data Average = Σfx/Σf ⇒ Average = 1145/35 = 32.7 ⇒ Range = Maximum frequency - minimum frequency = 8 - 2 ⇒ Range = 6 ∴ The range of frequency is below average India’s #1 Learning Platform Start Complete Exam Preparation
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Concept: Cumulative frequency:
Calculation: Given that, cumulative frequency of fifth observations is 8. Frequency of given observations are x - 2, x - 4, y, -2x, x Sum of frequencies = - 6 + y + x Since this sum will be equal to cumulative frequency up to 5th observations. ⇒ - 6 + y + x = 8 ⇒ y = 14 - x India’s #1 Learning Platform Start Complete Exam Preparation
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Concept: Cumulative frequency is the sum of all the previous frequencies up to the current point. The cumulative frequency is calculated by adding each frequency from a frequency distribution table to the sum of its predecessors. The last value will always be equal to the total for all observations since all frequencies will already have been added to the previous total. Also, Frequency of any class = cumulative frequency of class - cumulative frequency of preceding class Calculation: Let's calculate the frequency of each class using the cumulative frequencies of each class:
Clearly, we can see that 52 - 54 has the maximum frequency i.e.,14. Hence, 52 - 54 has the maximum frequency. India’s #1 Learning Platform Start Complete Exam Preparation
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Calculation Frequency distribution = frequency distribution is a list, table or graph that displays the frequency of various outcomes in a sample. In frequency distribution, the number of classes usually depends upon the size of the classes India’s #1 Learning Platform Start Complete Exam Preparation
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Concept:
Also, Frequency of any class=cumulative frequency of class - cumulative frequency of preceding class. Calculation: From the above discussion, we can calculate the frequency from the cumulative frequency as below.
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Given Frequency density is actually the frequency per unit width. Frequency of class interval 20 - 40 = 14 Formula used \(Frequency ~density = \frac{Frequency}{(upper ~limit – lower~ limit) } \) Calculation \(⇒\frac{14}{40-20}\) \(⇒\frac{14}{20}=0.7\) ∴ Frequency density is 0.7 India’s #1 Learning Platform Start Complete Exam Preparation
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Option 1 : Less than cumulative frequency
Given
Calculation
Cumulative frequency = 61 ∴ Frequency distribution is less than cumulative frequency
Cumulative frequency = it is the sum of the class and class below it in a frequency distribution India’s #1 Learning Platform Start Complete Exam Preparation
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Concept: In a pie chart, the central angle of each slice of the pie is proportional to its value as compared to the total value. θ = \(\rm \frac{\text{Value of Slice.}}{\text{Total Value.}}\times360^\circ\) Calculation: Angle corresponding to the Science graduates = θ = \(\rm \frac{\text{Number of Science graduates.}}{\text{Total number of graduates.}}\times360^\circ\). = \(\rm \frac{30}{30+70+50}\times360^\circ\) = \(\rm \frac{30}{150}\times360^\circ\) = 72°. India’s #1 Learning Platform Start Complete Exam Preparation
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Given Mid values = 30, 39, 48, 57, 66 Formula used Mid value of class interval = (L1 + L2)/2 L1 = Lower limit L2 = Upper limit Calculation For Second class mid value would be (L1 + L2)/2 Here L1 and L2 are Lower value and upper value of class interval Mid point of 30 and 39 = (L1 + L2)/2 ⇒ (30 + 39)/2 = 34.5 ⇒ Mid point of 39 and 48 ⇒ (39 + 48)/2 = 43.5 ⇒ Lower limit (L1 = 34.5) ⇒ Upper limit (L2 = 43.5) ∴ The second class of this distribution is 34.5 – 43.5
By options 1 – 34 – 44 Class size 44 – 34 = 10 39 – 30 =9 So size gap does not match so option 1 is wrong 2 – 34.5 – 43.5 Class size = 43.5 – 34.5 = 9 The mid point gap 39 – 30 = 9, 48 – 39 = 9, 57 – 48 = 9, and 66 – 57 = 9 So option (2) match with Class Size so option (2) is correct India’s #1 Learning Platform Start Complete Exam Preparation
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Screen savers do not reduce the use of power by your computer; once your screen saver kicks in, your monitor will draw its full power load. All users, whether on desktops or laptops, should configure their computers to use the power-saving or energy star modes that shut down power to the monitor, hard drive, and computer itself after periods of inactivity. Putting your computer in sleep mode allows it to use substantially less power, allows it to respond to some types of network activity, and allows you to not power off the computer. A computer display in full use gobbles up 65 watts – but still uses 25 watts when in sleep mode. When off it uses 0.8 watts. Setting computers, monitors, and copiers to use sleep-mode when not in use helps cut energy costs by approximately 40%. India’s #1 Learning Platform Start Complete Exam Preparation
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Explanation: Graphically mode can be determined by presenting the data in the form of a Histogram. The highest Histogram indicates the modal class. The intersection point of the lines diagonally joining the two top corners of the modal rectangles to the corners of the adjacent Histograms indicates the Modal Value. Hence, option (2) is correct.
Histogram - To find mode Ogives - To find median India’s #1 Learning Platform Start Complete Exam Preparation
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Calculation: Let the circle be the total number of students. Therefore 100% = 360° ⇒ 1% = \(\frac{{360^\circ }}{{100}}\) \(\therefore \;40\% \; = \frac{{360^\circ }}{{100}} \times 40 = 144^\circ\) India’s #1 Learning Platform Start Complete Exam Preparation
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Option 2 : the area of the rectangle.
Concept:
Calculation: From the definition of histogram, it is clear that the frequency of a class is proportional to the area of the rectangle, and NOT to its height. India’s #1 Learning Platform Start Complete Exam Preparation
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Option 1 : Discrete frequency distribution
The frequency distribution according to individual variate values is called Discrete frequency distribution. Concept: A discrete frequency distribution is a table that lists each number and the number of times (frequency) that it occurs in a list. The numbers are typically integers but they can be other step sizes provided that each number is an integral multiple of the step size. The following frequency distribution is classified: x: 5 15 38 47 68 y: 2 4 9 3 1 Here we can not find the relationship between the numbers 2, 4, 9, 3, and 1 hence, in this frequency distribution the values of the variable are determined individually.
Continuous frequency distribution: A continuous frequency distribution is a series in which the data are classified into different class intervals without gaps and their respective frequencies are assigned as per the class intervals and class width. Percentage frequency distribution: A percentage frequency distribution is a display of data that specifies the percentage of observations that exist for each data point or grouping of data points. India’s #1 Learning Platform Start Complete Exam Preparation
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Option 4 : Histogram and Ogive
Explanation In the determination of median graphically we adopt any of the two methods. In both the methods we draw ogives as per requirement. To calculate mode graphically a histogram of the given data is drawn at first. ∴ For determination of mode and median graphically, one considers Histogram and Ogive Bar diagram = A bar chart or bar graph is a chart or graph that presents categorical data with rectangular bars with heights or lengths proportional to the values that they represent. We can represent Mean on Bar graph Ogive = An ogive (oh-jive), sometimes called a cumulative frequency polygon, is a type of frequency polygon that shows cumulative frequencies. In other words, the cumulative percents are added on the graph from left to right. We represent partition value on ogive curve like median Line graph = line graph is a type of chart used to show information that changes over time. We plot line graphs using several points connected by straight lines. We also call it a line chart India’s #1 Learning Platform Start Complete Exam Preparation
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Explanation: Graphically, the median can be determined by the intersection point of Less than Ogive and More than Ogive. The value of the x-axis corresponding to the intersection point indicates the median. Hence, option (3) is correct.
Ogives - To find median Histogram - To find mode India’s #1 Learning Platform Start Complete Exam Preparation
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Data are information collected in a systematic manner with the aim of deriving certain related conclusion. Let us discuss the sources for the collection of data.
Hence, we conclude that the above statement is about arrayed data. India’s #1 Learning Platform Start Complete Exam Preparation
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In classification the data are arranged according to Ratios Differences Percentages Similarities
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