Welcome to Part 1 of our new 8-part series on Chapter 13, Statistics. This post contains the top 25 Multiple Choice Questions (MCQs) focusing on Mean, Median, Mode, and the Empirical Relationship between them.
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Top 25 MCQs - Statistics
Question 1: Empirical Relationship
The empirical relationship between the three measures of central tendency is:
Question 2: Modal Class
In a frequency distribution, the mid value of a class is 10 and the width of the class is 6. The lower limit of the class is:
Lower limit = Mid value - (h/2)
Lower limit = 10 - (6/2) = 10 - 3 = 7.
Question 3: Class Mark
The class mark of the class interval 10-25 is:
= (10 + 25) / 2 = 35 / 2 = 17.5.
Question 4: Median Class
Consider the following distribution:
Class: 0-5, 5-10, 10-15, 15-20, 20-25
Frequency: 10, 15, 12, 20, 9
The sum of lower limits of the median class and modal class is:
Modal Class: Max frequency is 20, so modal class is 15-20. Lower limit = 15.
Median Class: Total freq (N) = 10+15+12+20+9 = 66. N/2 = 33.
Cumulative Frequency: 10, 25, 37 (10-15 class covers up to 37). So median class is 10-15. Lower limit = 10.
Sum = 15 + 10 = 25.
Question 5: Ogive
The abscissa of the point of intersection of the 'less than type' and 'more than type' cumulative frequency curves of a grouped data gives its:
Question 6: Mean of First n Natural Numbers
The mean of first n natural numbers is:
Question 7: Mean Calculation
If the mean of the following distribution is 2.6, then the value of y is:
Variable (x): 1, 2, 3, 4, 5
Frequency (f): 4, 5, y, 1, 2
Σfx = (1*4) + (2*5) + (3*y) + (4*1) + (5*2) = 4 + 10 + 3y + 4 + 10 = 28 + 3y.
Σf = 4 + 5 + y + 1 + 2 = 12 + y.
2.6 = (28 + 3y) / (12 + y)
31.2 + 2.6y = 28 + 3y
3.2 = 0.4y => y = 8.
Question 8: Mode Value
The mode of the data: 15, 16, 17, 16, 15, 17, 16, 15, 15 is:
15 appears 4 times. 16 appears 3 times. 17 appears 2 times.
So, mode is 15.
Question 9: Median Formula
The formula to find the median of grouped data is:
Question 10: Empirical Relation Application
If the mode of a distribution is 8 and its mean is 8, then its median is:
3 Median = 8 + 2(8) = 24
Median = 24 / 3 = 8. (Note: For a symmetric distribution, Mean = Median = Mode).
Question 11: Mean of Primes
The mean of the first five prime numbers is:
Sum = 2+3+5+7+11 = 28.
Mean = 28 / 5 = 5.6.
Question 12: Cumulative Frequency
Cumulative frequency curve is also known as:
Question 13: Range
The range of the data: 15, 20, 6, 5, 30, 35, 90 is:
Max = 90, Min = 5.
Range = 90 - 5 = 85.
Question 14: Median from Data
The median of the following data: 20, 25, 15, 30, 10, 35, 40 is:
Number of terms n = 7 (odd).
Median = ((n+1)/2)th term = 4th term = 25.
Question 15: Upper Limit of Modal Class
For the following distribution:
Class: 0-5, 5-10, 10-15, 15-20, 20-25
Frequency: 10, 15, 12, 20, 9
The upper limit of the modal class is:
Question 16: Mean of x
If the mean of x, x+3, x+6, x+9, and x+12 is 10, then x is:
Sum = 5x + 30. n = 5.
10 = (5x + 30) / 5
50 = 5x + 30
20 = 5x => x = 4.
Question 17: Mode Formula Term
In the formula for mode: l + [(f1 - f0)/(2f1 - f0 - f2)] × h, f0 represents:
Question 18: Relationship x, y, z
If the mean, mode, and median of a frequency distribution are x, y, and z respectively, then the correct relationship is:
Substitute symbols: y = 3z - 2x.
Question 19: Cumulative Freq Utility
Construction of a cumulative frequency table is useful in determining the:
Question 20: Assumed Mean Method
In the assumed mean method for finding the mean, the deviation 'd' is calculated as:
Question 21: Measure for Open-End
Which measure of central tendency can be determined graphically?
Question 22: Median Class Upper Limit
For the following data, the upper limit of the median class is:
Class: 0-10, 10-20, 20-30, 30-40, 40-50
Freq: 4, 6, 10, 3, 2
CF: 4, 10, 20, 23, 25.
12.5 lies in the class with CF 20 (which covers 11 to 20).
The class is 20-30. Upper limit is 30.
Question 23: Mode Calculation
If Mean = 20 and Median = 22, then Mode is:
Mode = 3(22) - 2(20)
Mode = 66 - 40 = 26.
Question 24: Mean Invariance
If each observation of a data is increased by 5, then their mean:
Question 25: Class Mark Formula
In the formula x̄ = a + (Σfiui / Σfi) × h, ui is:
