Chapter:

30+ Unit 1 Solved MCQs

in Business Statistics

These multiple-choice questions (MCQs) are designed to enhance your knowledge and understanding in the following areas: Bachelor of Commerce (B Com) .

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Chapter: Unit 1

1.	The sum of deviations of observations from their arithmetic mean:
A.	Maximum
B.	Least
C.	Zero
D.	None of these
Answer» C. Zero

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2.	The sum of absolute deviations is minimum when taken from:
A.	Mean
B.	Median
C.	Mode
D.	None of these
Answer» B. Median

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3.	The sum of squared deviations is minimum when taken from:
A.	Mean
B.	Median
C.	Mode
D.	None of these
Answer» A. Mean

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4.	What is the median of 33, 86, 68, 32, 80, 48, 70?
A.	32
B.	68
C.	80
D.	86
Answer» B. 68
Explanation: To find the median of a set of numbers, you first need to order the numbers in ascending or descending order. {32, 33, 48, 68, 70, 80, 86} The median is the middle value when a data set has an odd number of observations. The middle value of 7 numbers is the 4th one, which is 68. So, the median of this set is 68.

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5.	In a moderately skewed distribution, the value of mean is 16 and that of mode is 25.
A.	20
B.	19
C.	21
D.	None of these
Answer» B. 19

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6.	In a moderately skewed distribution, the following equation indicates the relationship among mean, median and mode:
A.	Mean = 2 Mode - 3 Median
B.	Mode = 3 Median – 2 Mean
C.	Median = 3 Mean – 2 Mode
D.	None of these
Answer» B. Mode = 3 Median – 2 Mean

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7.	For a symmetrical distribution, Q1 and Q3 are 20 and 60 respectively. The value of median will be:
A.	20
B.	30
C.	40
D.	50
Answer» C. 40

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8.	The variate values which divide a series into ten equal parts are called:
A.	Quartiles
B.	Deciles
C.	Percentiles
D.	None of these
Answer» B. Deciles

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9.	From which average, the sum of deviations is zero?
A.	Mean
B.	Median
C.	Mode
D.	None of these
Answer» A. Mean

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10.	The average to be used to determine the average size of the shoe sold in a shop is:
A.	Mean
B.	Median
C.	Mode
D.	None of these
Answer» C. Mode

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11.	Find the Mode of 5, 3, 27, 5, 9, 3, 8, 5:
A.	5
B.	27
C.	9
D.	3
Answer» A. 5

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12.	In a moderately asymmetrical distribution, the value of mean is 75 and the value of mode is 60:
A.	75
B.	70
C.	85
D.	80
Answer» B. 70

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13.	Given Mean = 70.2 and mode = 70.5. Find the median using empirical relationship among them.
A.	120
B.	150
C.	180
D.	300
Answer» B. 150

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14.	In a moderately skewed distribution, the value of mode is 120 and that of median is 140. Find the value of arithmetic mean.
A.	150
B.	160
C.	170
D.	180
Answer» A. 150

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15.	The arithmetic mean of the marks obtained by 50 students was calculated as 44. It was later discovered that a score of 36 was misread as 56. Find the correct value of arithmetic mean of the marks obtained by the students.
A.	43
B.	43.6
C.	45
D.	50
Answer» B. 43.6

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16.	The marks obtained by 9 students in a test are 25, 20, 15, 45, 18, 7, 10, 38 and 12. Find the median.
A.	38
B.	20
C.	18
D.	15
Answer» C. 18

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17.	In a moderately asymmetrical distribution, the mode and mean are 32.1 and 35.4 respectively. Calculate the median.
A.	35
B.	34.3
C.	36
D.	37
Answer» B. 34.3

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18.	In a moderately skewed distribution, the mode and median are 20 and 24 respectively. Calculate the value of mean.
A.	27
B.	26
C.	25
D.	28
Answer» B. 26

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19.	The mean weight of 150 students in a class is 60 Kg. The mean weight of Boy students is 70 Kg and that of a girl students is 55 kg. Find the number of Boys and Girls in the class.
A.	50 and 100
B.	100 and 50
C.	150 and 200
D.	200 and 150
Answer» A. 50 and 100

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20.	A distribution consists of three components with total frequencies of 200, 250 and 300 having means 25, 10 and 15 respectively. Find the mean of the combined distribution.
A.	17
B.	16
C.	15
D.	20
Answer» B. 16

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21.	The arithmetic mean is 12 and the number of observations are 20 then the sum of all the values is
A.	8
B.	32
C.	240
D.	1.667
Answer» C. 240

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22.	The method used to compute average or central value of the collected data is considered as
A.	measures of positive variation
B.	measures of central tendency
C.	measures of negative skewness
D.	measures of negative variation
Answer» B. measures of central tendency

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23.	The mean or average used to measure central tendency is called
A.	sample mean
B.	arithmetic mean
C.	negative mean
D.	population mean
Answer» B. arithmetic mean

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24.	If the mean of percentages, rates and ratios is to be calculated then the central tendency measure which must be used in this situation is
A.	weighted arithmetic mean
B.	paired arithmetic mean
C.	non-paired arithmetic mean
D.	square of arithmetic mean
Answer» A. weighted arithmetic mean

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25.	In the quartiles, the central tendency median to be measured must lie in
A.	first quartile
B.	second quartile
C.	third quartile
D.	four quartile
Answer» B. second quartile

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26.	A numerical value used as a summary measure for a sample, such as sample mean, is known as a
A.	population parameter
B.	sample parameter
C.	sample statistic
D.	population mean
Answer» C. sample statistic

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27.	The mean of a sample is
A.	always equal to the mean of the population
B.	always smaller than the mean of the population
C.	computed by summing the data values and dividing the sum by (n - 1)
D.	computed by summing all the data values and dividing the sum by the number of items
Answer» D. computed by summing all the data values and dividing the sum by the number of items

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28.	In a five number summary, which of the following is not used for data summarization?
A.	the smallest value
B.	the largest value
C.	the median
D.	the 25th percentile
Answer» D. the 25th percentile

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29.	Since the mode is the most frequently occurring data value, it
A.	can never be larger than the mean
B.	is always larger than the median
C.	is always larger than the mean
D.	None of the above
Answer» C. is always larger than the mean

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30.	In statistics out of 100, marks of 21 students in final exams are as 90, 95, 95, 94, 90, 85, 84, 83, 85, 81, 92, 93, 82, 78, 79, 81, 80, 82, 85, 76, 85 then mode of data is
A.	85
B.	95
C.	90
D.	81
Answer» A. 85

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31.	Branches of statistics includes
A.	applied statistics
B.	mathematical statistics
C.	industry statistics
D.	both a and b
Answer» D. both a and b

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32.	What is the median of the data 78, 56, 22, 34, 45, 54, 39, 68, 54, 84?
A.	54
B.	53
C.	55
D.	51
Answer» A. 54

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33.	Find the mean of x + 77, x + 7, x + 5, x + 3 and x – 2?
A.	x + 8
B.	x + 18
C.	x – 8
D.	x – 18
Answer» B. x + 18

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34.	In the class intervals 40 – 50, 50 – 60, the number 50 is included in which of the following?
A.	40 – 50
B.	30 – 40
C.	50 – 60
D.	60 – 70
Answer» C. 50 – 60

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35.	If each observation of the data is increased by 5, then what happens to its mean?
A.	is increased by 4
B.	is increased by 5
C.	is decreased by 4
D.	is decreased by 5
Answer» B. is increased by 5

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30+ Unit 1 Solved MCQs

The sum of deviations of observations from their arithmetic mean:

The sum of absolute deviations is minimum when taken from:

The sum of squared deviations is minimum when taken from:

What is the median of 33, 86, 68, 32, 80, 48, 70?

In a moderately skewed distribution, the value of mean is 16 and that of mode is 25.

In a moderately skewed distribution, the following equation indicates the relationship among mean, median and mode:

For a symmetrical distribution, Q1 and Q3 are 20 and 60 respectively. The value of median will be:

The variate values which divide a series into ten equal parts are called:

From which average, the sum of deviations is zero?

The average to be used to determine the average size of the shoe sold in a shop is:

Find the Mode of 5, 3, 27, 5, 9, 3, 8, 5:

In a moderately asymmetrical distribution, the value of mean is 75 and the value of mode is 60:

Given Mean = 70.2 and mode = 70.5. Find the median using empirical relationship among them.

In a moderately skewed distribution, the value of mode is 120 and that of median is 140. Find the value of arithmetic mean.

The arithmetic mean of the marks obtained by 50 students was calculated as 44. It was later discovered that a score of 36 was misread as 56. Find the correct value of arithmetic mean of the marks obtained by the students.

The marks obtained by 9 students in a test are 25, 20, 15, 45, 18, 7, 10, 38 and 12. Find the median.

In a moderately asymmetrical distribution, the mode and mean are 32.1 and 35.4 respectively. Calculate the median.

In a moderately skewed distribution, the mode and median are 20 and 24 respectively. Calculate the value of mean.

The mean weight of 150 students in a class is 60 Kg. The mean weight of Boy students is 70 Kg and that of a girl students is 55 kg. Find the number of Boys and Girls in the class.

A distribution consists of three components with total frequencies of 200, 250 and 300 having means 25, 10 and 15 respectively. Find the mean of the combined distribution.

The arithmetic mean is 12 and the number of observations are 20 then the sum of all the values is

The method used to compute average or central value of the collected data is considered as

The mean or average used to measure central tendency is called

If the mean of percentages, rates and ratios is to be calculated then the central tendency measure which must be used in this situation is

In the quartiles, the central tendency median to be measured must lie in

A numerical value used as a summary measure for a sample, such as sample mean, is known as a

The mean of a sample is

In a five number summary, which of the following is not used for data summarization?

Since the mode is the most frequently occurring data value, it

In statistics out of 100, marks of 21 students in final exams are as 90, 95, 95, 94, 90, 85, 84, 83, 85, 81, 92, 93, 82, 78, 79, 81, 80, 82, 85, 76, 85 then mode of data is

Branches of statistics includes

What is the median of the data 78, 56, 22, 34, 45, 54, 39, 68, 54, 84?

Find the mean of x + 77, x + 7, x + 5, x + 3 and x – 2?

In the class intervals 40 – 50, 50 – 60, the number 50 is included in which of the following?

If each observation of the data is increased by 5, then what happens to its mean?