13. Statistics

*नोट: यह सेक्शन रिवीजन के लिए है। अपना ज्ञान परखने के लिए ऊपर दिए गए क्विज़ में भाग लें।

1. The mean of the first five natural numbers is?
   A) 2  |  B) 3  |  C) 4  |  D) 5
2. Which of the following is not a measure of central tendency?
   A) Mean  |  B) Median  |  C) Mode  |  D) Range
3. The empirical relationship between Mean, Median, and Mode is given by?
   A) 3 Median = Mode + 2 Mean  |  B) 2 Median = Mode + 3 Mean  |  C) Mode = 3 Mean - 2 Median  |  D) Mean = 3 Median - 2 Mode
4. The cumulative frequency curve is also commonly known as?
   A) Histogram  |  B) Frequency Polygon  |  C) Ogive  |  D) Bar Graph
5. The value of the variable which occurs most frequently in a distribution is called?
   A) Mean  |  B) Median  |  C) Mode  |  D) Frequency
6. What is the class mark of the class interval 10-25?
   A) 15  |  B) 17.5  |  C) 20  |  D) 22.5
7. In the formula of mode for grouped data, what does the variable h represent?
   A) Lower limit of modal class  |  B) Frequency of modal class  |  C) Size of the class interval  |  D) Cumulative frequency
8. For finding the median of grouped data, which specific column do we need to calculate?
   A) Class marks  |  B) Cumulative frequency  |  C) Assumed mean  |  D) Step deviations
9. The mean of 10 observations is 15. If each observation is increased by 2, what will be the new mean?
   A) 15  |  B) 17  |  C) 20  |  D) 30
10. The sum of all frequencies in a given frequency distribution is generally denoted by?
    A) N  |  B) x  |  C) d  |  D) h
11. If the mode of a data is 18 and the mean is 24, then what is the value of the median?
    A) 20  |  B) 21  |  C) 22  |  D) 24
12. The abscissa of the point of intersection of the less than type and of the more than type ogives gives its?
    A) Mean  |  B) Median  |  C) Mode  |  D) Deviation
13. If the arithmetic mean of 7, 8, x, 11, 14 is exactly x, then the value of x is?
    A) 8  |  B) 9  |  C) 10  |  D) 11
14. Construction of a cumulative frequency table is primarily useful in determining the?
    A) Mean  |  B) Median  |  C) Mode  |  D) Standard Deviation
15. While computing the mean of grouped data, we assume that the frequencies are?
    A) Evenly distributed  |  B) Centered at the classmarks  |  C) Centered at the lower limits  |  D) Centered at the upper limits
16. For the following classes 0-5, 5-10, 10-15, 15-20 with frequencies 10, 15, 12, 20 respectively, what is the upper limit of the median class?
    A) 10  |  B) 15  |  C) 20  |  D) 5
17. If xi are the midpoints of the class intervals, fi are the corresponding frequencies, and m is the mean, then the sum of fi(xi - m) is equal to?
    A) 0  |  B) 1  |  C) -1  |  D) m
18. Consider the classes 10-19, 20-29, 30-39. What is the true lower limit of the class 20-29?
    A) 20  |  B) 19  |  C) 19.5  |  D) 20.5
19. The step-deviation method for finding mean is particularly useful when the class intervals have?
    A) Different widths  |  B) Equal widths and large numerical values  |  C) Small numerical values  |  D) No class marks
20. In a grouped frequency distribution, the assumed mean method formula uses di. What does di represent?
    A) xi - a  |  B) xi + a  |  C) a - xi  |  D) xi / a
21. The mean of 100 observations is 50. If one observation 50 is accidentally replaced by 150, what will be the correct new mean?
    A) 50.5  |  B) 51  |  C) 52  |  D) 55
22. In a continuous frequency distribution, the median of the data is 24. If each item is increased by 2, what is the new median?
    A) 24  |  B) 26  |  C) 22  |  D) 48
23. Which measure of central tendency cannot be determined geographically or graphically?
    A) Mean  |  B) Median  |  C) Mode  |  D) Quartile
24. If the median of a frequency distribution is 28.5 and the total frequency is 60, finding missing frequencies x and y requires how many distinct equations?
    A) One  |  B) Two  |  C) Three  |  D) Four
25. If the sum of frequencies is 24, and the calculated mean is 50, what is the total sum of the product of frequencies and class marks (sum fi xi)?
    A) 1000  |  B) 1200  |  C) 1400  |  D) 2400
26. The mean of the first n odd natural numbers is always equal to?
    A) n  |  B) n+1  |  C) n/2  |  D) n-1
27. For a given skewed distribution, if the mean is 30 and the median is 32, what is the approximate calculated value of the mode?
    A) 34  |  B) 35  |  C) 36  |  D) 38
28. In the standard formula for finding the median, what does the term cf specifically denote?
    A) Cumulative frequency of the median class  |  B) Cumulative frequency of the class preceding the median class  |  C) Frequency of the median class  |  D) Cumulative frequency of the class succeeding the median class
29. If an ogive curve is drawn for a given statistical data, what does the y-axis strictly represent?
    A) Class Limits  |  B) Class Marks  |  C) Frequencies  |  D) Cumulative Frequencies
30. If the mean of x, x+3, x+6, x+9, and x+12 is 10, then what is the value of x?
    A) 3  |  B) 4  |  C) 5  |  D) 6