Measures of Central Tendency (Mean, Median, Mode)

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JEE Main 2015

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The mean of the data set comprising of 16 observations is 16. If one of the observation valued 16 is deleted and three new observations valued 3, 4 and 5 are added to the data, then the mean of the resultant data, is:

The average marks of boys in class is 52 and that of girls is 42. The average marks of boys and girls combined is 50. The percentage of boys in the class is

If in a frequency distribution, the mean and median are 21 and 22 respectively, then its mode is approximately

The median of a set of 9 distinct observations is 20.5. If each of the largest 4 observations of the set is increased by 2, then the median of the new set

(A)

remains the same as that of the original set

is two times the original median.

JEE Main 2002

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In a class of 100 students there are 70 boys whose average marks in a subject are 75. If the average marks of the complete class is 72, then what is the average marks of the girls?

A variable takes value $x$ with frequency $^{n + x - 1} C_{x}$ , $x = 0, 1, 2, \dots, n$ . The mode of the variable is .........

JEE Main 2018 (15 April Shift 1)

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The mean of a set of 30 observations is 75. If each observation is multiplied by a non-zero number $λ$ and then each of them is decreased by 25, their mean remains the same. Then $λ$ is equal to

JEE Main 2019 (12 January Shift 1)

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If the sum of the deviations of 50 observations from 30 is 50, then the mean of these observation is :

JEE Main 2019 (10 April Shift 1)

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If for some $x \in R$ , the frequency distribution of the marks obtained by 20 students in a test is : Marks 2, 3, 5, 7; Frequency $(x + 1)^{2}, 2 x - 5, x^{2} - 3 x, x$ . then the mean of the marks is :

JEE Main 2020 - 6 Sep (Evening)

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Consider the data on $x$ taking the values $0, 2, 4, 8, \dots, 2^{n}$ with frequencies $^{n} C_{0},^{n} C_{1},^{n} C_{2}, \dots,^{n} C_{n}$ respectively. If the mean of this data is $\frac{728}{2 ^{n}}$ then $n$ is equal to

JEE Main 2021 (31 Aug Shift 1)

LEVELJEE Main

The mean of 10 numbers $7 \times 8, 10 \times 10, 13 \times 12, 16 \times 14, \dots$ is .

JEE Main 2021 (22 July Shift 1)

LEVELJEE Main

Consider the following frequency distribution: $Class : Frequency : 0 - 6 a 6 - 12 b 12 - 18 12 18 - 24 9 24 - 30 5$ If mean = $\frac{309}{22}$ and median = 14, then the value $(a - b)^{2}$ is equal to _____.

JEE Main 2021 (25 July Shift 1)

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Consider the following frequency distribution $c l a ss : F r e q u e n cy : 10 - 20 α 20 - 30 110 30 - 40 54 40 - 50 30 50 - 60 β$ If the sum of all frequencies is 584 and median is 45, then $∣ α - β ∣$ is equal to

JEE Main 2021 (March)

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The mean age of 25 teachers in a school is 40 years. A teacher retires at the age of 60 years and a new teacher is appointed in his place. If the mean age of the teachers in this school now is 39 years, then the age (in years) of the newly appointed teacher is ______.

JEE Main 2024 (30 Jan Shift 1)

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Let $M$ denote the median of the following frequency distribution. $Class Frequency 0 - 4 3 4 - 8 9 8 - 12 10 12 - 16 8 16 - 20 6$ Then $20 M$ is equal to :

JEE Main 2025 (January)

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Marks obtains by all the students of class 12 are presented in a freqency distribution with classes of equal width. Let the median of this grouped data be 14 with median class interval 12-18 and median class frequency 12. If the number of students whose marks are less than 12 is 18, then the total number of students is

The mean of the data set comprising of 16 observations is 16. If one of the observation valued 16 is deleted and three new observations valued 3, 4 and 5 are added to the data, then the mean of the resultant data, is:

The average marks of boys in class is 52 and that of girls is 42. The average marks of boys and girls combined is 50. The percentage of boys in the class is

If in a frequency distribution, the mean and median are 21 and 22 respectively, then its mode is approximately

The median of a set of 9 distinct observations is 20.5. If each of the largest 4 observations of the set is increased by 2, then the median of the new set

In a class of 100 students there are 70 boys whose average marks in a subject are 75. If the average marks of the complete class is 72, then what is the average marks of the girls?

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A variable takes value x with frequency n+x−1Cx​, x=0,1,2,…,n. The mode of the variable is .........

If the sum of the deviations of 50 observations from 30 is 50, then the mean of these observation is :

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Consider the data on x taking the values 0,2,4,8,…,2n with frequencies nC0​,nC1​,nC2​,…,nCn​ respectively. If the mean of this data is 2n728​ then n is equal to

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The mean of 10 numbers 7×8,10×10,13×12,16×14,… is .

The mean age of 25 teachers in a school is 40 years. A teacher retires at the age of 60 years and a new teacher is appointed in his place. If the mean age of the teachers in this school now is 39 years, then the age (in years) of the newly appointed teacher is ______.

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Let M denote the median of the following frequency distribution. ClassFrequency​0−43​4−89​8−1210​12−168​16−206​​ Then 20M is equal to :

A variable takes value $x$ with frequency $^{n + x - 1} C_{x}$ , $x = 0, 1, 2, \dots, n$ . The mode of the variable is .........

Consider the data on $x$ taking the values $0, 2, 4, 8, \dots, 2^{n}$ with frequencies $^{n} C_{0},^{n} C_{1},^{n} C_{2}, \dots,^{n} C_{n}$ respectively. If the mean of this data is $\frac{728}{2 ^{n}}$ then $n$ is equal to

The mean of 10 numbers $7 \times 8, 10 \times 10, 13 \times 12, 16 \times 14, \dots$ is .

Let $M$ denote the median of the following frequency distribution. $Class Frequency 0 - 4 3 4 - 8 9 8 - 12 10 12 - 16 8 16 - 20 6$ Then $20 M$ is equal to :