Statistics MCQ

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Statistics is a branch of mathematics that deals with the study of data collection, analysis, interpretation, presentation, and organization. The field is widely used to acquire a better understanding of data and to focus on its applications. In other words, statistics is the process of collecting, evaluating, and summarising information or data into a mathematical form. Statistics deals with various concepts like data representation, measures of central tendency- mean, median and mode, measures of dispersion, probability etc. there are two statistical approaches in mathematics- descriptive and inferential statistics.

Also read: Statistics Revision Notes

Multiple Choice Questions

Ques 1. If the mean of frequency distribution is 6.5 and ∑fi xi = 120 + 2k, ∑fi = 20, then k is equal to:

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Ans: c 5

Explanation: As per the given question,

X_mean= ∑fi xi /∑fi

6.5 = (120+2k)/20

130 = 120+2k

2k = 130-120

2k= 10

k=5

Ques 2. If x₁, x₂, x₃,….., x_n are the observations of a given data. Then the mean of the observations will be:

Total number of observations/Sum of observations
Sum of observations/Total number of observations
Sum of observations +Total number of observations
None of the above

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Ans: (b) Sum of observations/Total number of observations

Explanation: The mean or average of observations will be equal to the ratio of sum of observations and total number (n) of observations.

x_mean=x₁+x₂+x₃+…..+x_n/n

Ques 3. The mode and mean are given by 5 and 6, respectively. Then the median is:

17/3
13/3
23/3
33

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Ans: (a) 17/3

Explanation: Using Empirical formula,

Mode = 3Median – 2 Mean

3Median = Mode+2 Mean

Median = (Mode+2Mean)/3

Median = (5+2(6))/3 = (5+12)/3 = 17/3

Ques 4. The mean of the data: 4, 11, 5, 8, 12 is;

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Ans: (b) 8

Explanation: For n values in a set of data namely as x₁, x_2,x_{3, …}x_n, the mean of data is given as:

Arithmetic Mean

Therefore, Mean = (4+11+5+8+12)/5 = 40/5 = 8

Ques 5. The median of the data 11,12, 14, 17, 20, 27 is:

30/2
3½
33/2
35/2

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Ans: (b) 31/2

Explanation: For the given data, there are two middle terms, 14 and 19.

Hence, median = (14+17)/2 = 31 /2

Ques 6. Find the mean of frequency distribution, if ∑f_i x_i = 110, and ∑f_i = 10, then k is equal to:

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Ans: (d) 11

Explanation: As per the given question,

X_mean= ∑f_i x_i /∑f_i

= (110)/10

= 11

Therefore, the mean of the frequency distribution is 11.

Ques 7. The mean and median are given by 4 and 12, respectively. Then the mode is:

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Ans: (a) 28

Explanation: Using Empirical formula,

Mode = 3Median – 2 Mean

= (3 x 12)- 2 x 4

= 36- 8

= 28

Ques 8. If the mean of first n natural numbers is 4n/6, then the value of n is:

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Ans: (d)

Explanation: Sum of natural numbers = n(n + 1)/2

Given, mean = 4n/6

Mean = sum of natural numbers/n

4n/6 = n(n + 1)/2n

4n/6 = (n + 1)/2

8n = 6n + 6

n = 3

Ques 9. If the mean of a, a+2, a+4, a+8 and a+11 is 10, then a is equal to;

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Ans: (c) 5

Explanation: Mean = 10

(a + a + 2 + a + 4 + a + 8 + a + 11)/5 = 10

5a + 25 = 50

5a = 25

a = 5

Ques 10. The class interval of a given observation is 5 to 10, then the class mark for this interval will be:

7.5
13.5
8
14.5

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Ans: (a) 7.5

Explanation: Class mark = (Upper limit + Lower limit)/2

= (10 + 5)/2

= 15/2

= 7.5

Ques 11. If the sum of frequencies is 30, then the value of x in the observation: x, 5,6,1,2, will be;

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Ans: (b) 16

Explanation:

Given,

∑f_i = 30

∑f_i = x + 5 + 6 + 1 + 2 = 14 + x

30 = 14 + x

x = 30 – 14 = 16

Also Read:

Important Concepts
Types of Data in Statistics	T Test Table	Statistical Inference
Mean Deviation Continuous Frequency Distribution	Frequency Distribution Table Statistics	Standard Deviation
Variance	Difference Between ln and log	Difference Between Mean and Median
Difference Between Average and Mean	Difference Between Variance and Standard Deviation	Statistics Formula

Ques 12. The cumulative frequency curve is also called

Ogive
Histogram
Bar graph
Median

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Ans: (a) ogive

Explanation: Ogive

A cumulative frequency curve is a graphical representation of the cumulative frequencies of a given data. It is called ogive. An ogive can either be less than ogive or more than ogive.

Less Than Ogive

Less than ogive is a graphical representation of the frequency table, where the cumulative frequency starts from the total of the frequency and moves on to the lowest frequency.

More than Ogive

More than ogive is a graphical representation of the frequency table, where the cumulative frequency starts from the lowest frequency and moves on to the total of the frequencies.

Ques 13. If the sum of frequencies is 36, then the value of x in the observation: x, 4,6,1,5, will be:

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Ans: (b) 10

Explanation:

Given,

∑fi = 36

∑fi = x+4+6+1+5=16+x

36 = 16+x

x=36-16 = 10

Ques 14. The relationship between the measure of central tendency- mean, median and mode for a moderately skewed distribution is given as:

mode = 3 median – 2 mean
mode = median – 2 mean
mode = 2 median – 3 mean
mode = median – mean

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Ans: (a)mode = 3 median – 2 mean

Explanation: the relation between or empirical formula for the measure of central tendency- mean, median and mode is given as:

Mode = 3 median – 2 mean

Mean= (3 median-mode)/2

Median= (mode- 2 mean)/3

Ques 15. Mode and mean of the data are 6k and 12k. Median of the data is

12k
10k
15k
16k

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Ans: (b) 10k

Explanation:

The relation between mean, median, and mode is given as:

Mode = 3 median – 2 mean

Therefore, 6k = 3 median – 2 × 12k

3 median = 24k + 6k

Median= 30k/3 ⇒ Median = 10k.

Ques 16. Mean of n numbers x₁, x₂, x₃… x_n is m. If x_n is replaced by x, then new mean is

m – x_n + x
(m−xn+xn)/n
(n−1)m+xn
(nm−xn+xn)/n

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Ans: (d) (nm−xn+xn)/n

Explanation:
MCQ Questions for Class 10 Maths Chapter 14 Statistics with Answers

Ques. The mean of the following distribution is

x_i	11	14	17	20
f_i	2	6	8	5

12.6
15
16.2
18.4

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Ans: (c) 16.2

Explanation:

x_i	f_i	f_ix_i
11	2	22
14	6	84
17	8	136
20	5	100
	∑fi = 21	∑fi xi=342

x_mean = ∑fi xi/∑fi

= 342/21 = 16.2

Ques. Consider the following frequency distribution of the heights of 60 students in a class:

Height (in cm)	150 – 155	155 – 160	160 – 165	165 – 170	170 – 175	175 – 180
Number of students	15	13	10	8	9	5

The sum of the lower limit of the modal class and the upper limit of the median class is:

315
310
320
330

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Ans: (a) 315

Explanation:

Height (in cm)	150 – 155	155 – 160	160 – 165	165 – 170	170 – 175	175 – 180
Number of students	15	13	10	8	9	5
Cumulative frequency	15	28	38	46	55	60

N/2 = (15+ 13+ 10+ 8+ 9+ 5)/2= 60/2 = 30

The cumulative frequency nearer and greater than 30 is 38 which corresponds to the class interval 160 – 165.

Thus, median class = 160 – 165

The upper limit of median class = 165

Highest frequency = 15

So, the modal class = 150 – 155

The lower limit of modal class = 150

Therefore, the sum of the lower limit of the modal class and the upper limit of the median class = 150 + 165 = 315

Ques 17. What is the ratio of the sum of observations and the total number of observations called?

Median
Mode
Mean
Central Tendency

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Ans. c

Explanantion: In a set of given data, a single value representative of entire set of data is called a measure of central tendency.

There are three important measures of central tendency - mean, median, and mode.

Mode is the most recurring value of the given data set.
Median is the central value of the given data set.
Mean is the average of the given gives of the data set. It can be calculated as the sum of all the observations divided by the total number of observations.

Ques 18. The median of the data: 17, 2, 7, 27, 15, 5, 14, 8, 10, 24, 48, 10, 8, 7, 18, 28 is:

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Ans. b

Explanation: Arrange the given data in ascending order:

2, 5, 7, 7, 8, 8, 10, 10, 14, 15, 17, 18, 24, 27, 28, 48

Since, the number of observations givere here is even, hence,

Median will be average of two middle terms.

n/2th = 16/2 = 8th term

(n/2 +1)th = (16/2 + 1)th = 9th term

Therefore,

Median = (10+14)/2 = 12

Ques 19: Mean of the data 2, 3, 4, 5, 0, 1, 3, 3, 4, 3 is:

2
2.6
2.8
2.2

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Ans. c

Explanation: Mean = (2+3+4+5+0+1+3+3+4+3)/10 = 28/10 = 2.8

Ques 20. What is the class mark of the class interval 90-120?

115
90
105
125

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Ans. c

Explanation: Class mark = (upper limit + lower limit)/2

Class mark = (120+90)/2

Class mark = 105

Ques 21. Calcultate mode of the following data: 15, 14, 19, 20, 14, 15, 16, 14, 15, 18, 14, 19, 15, 17, 15.

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Ans. a

Explanation: Mode of the data 15, 14, 19, 20, 14, 15, 16, 14, 15, 18, 14, 19, 15, 17, 15 is 15, because the number 15 is repeated 5 times.

Ques 22. What is the difference between maximum and minimum values of a given observation called?

Class Interval
Range
Class
Classmark

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Ans. b

Explanation: Difference between the maximum and minimum values of the given observation is called range.

Also Read:

Chapter Related Concepts
Variance Formula	Mean Deviation Formula	Interquartile Range Formula
Weighted Mean Formula	Statistical Physics	Mean Absolute Deviation
Root Mean Square	Standard Error Formula	Skewness Formula
Chi Square Formula	Coefficient of Variation Formula	Correlation Coefficient Formula

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Monthly consumption (in units)	Number of consumers
65 - 85	4
85 - 105	5
105 - 125	13
125 - 145	20
145 - 165	14
165 - 185	8
185 - 205	4

Statistics MCQ

Multiple Choice Questions

CBSE X Related Questions

1.
A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle of elevation from his eyes to the top of the building increases from 30° to 60° as he walks towards the building. Find the distance he walked towards the building.

2.
The angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation of the top of the tower from the foot of the building is 60°. If the tower is 50 m high, find the height of the building.

4.
A vertical pole of length 6 m casts a shadow 4 m long on the ground and at the same time a tower casts a shadow 28 m long. Find the height of the tower.

5.
If 3 cot A = 4, check whether \(\frac{(1-\text{tan}^2 A)}{(1+\text{tan}^2 A)}\) = cos² A – sin²A or not

Similar Mathematics Concepts

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Statistics MCQ

Multiple Choice Questions

CBSE X Related Questions

1. A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle of elevation from his eyes to the top of the building increases from 30° to 60° as he walks towards the building. Find the distance he walked towards the building.

2. The angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation of the top of the tower from the foot of the building is 60°. If the tower is 50 m high, find the height of the building.

3. The following frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Find the median, mean and mode of the data and compare themMonthly consumption (in units) Number of consumers65 - 85 485 - 1055105 - 12513125 - 14520145 - 16514165 - 1858185 - 2054

4. A vertical pole of length 6 m casts a shadow 4 m long on the ground and at the same time a tower casts a shadow 28 m long. Find the height of the tower.

5. If 3 cot A = 4, check whether \(\frac{(1-\text{tan}^2 A)}{(1+\text{tan}^2 A)}\) = cos2 A – sin2 A or not

Similar Mathematics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle of elevation from his eyes to the top of the building increases from 30° to 60° as he walks towards the building. Find the distance he walked towards the building.

2.
The angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation of the top of the tower from the foot of the building is 60°. If the tower is 50 m high, find the height of the building.

4.
A vertical pole of length 6 m casts a shadow 4 m long on the ground and at the same time a tower casts a shadow 28 m long. Find the height of the tower.

5.
If 3 cot A = 4, check whether \(\frac{(1-\text{tan}^2 A)}{(1+\text{tan}^2 A)}\) = cos² A – sin²A or not