Mathematics

Classified and Ungrouped Data

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Udyog Nirikshak-24.06.2018

MEDIUM

If the mean of a, b, c is $M_1$ and the mean of $a^2, b^2, c^2$ is $M_2$ , then a mean of ab, bc and ca is-

\frac{M_1^2 - 3M_2}{3}

\frac{3M_1^2 - 2M_2}{2}

\frac{3M_1^2 - M_2}{2}

\frac{3M_1^2 - M_1}{3}

Explanation

Given $a+b+c = 3M_1$ and $a^2+b^2+c^2 = 3M_2$ . $(a+b+c)^2 = 9M_1^2 = a^2+b^2+c^2 + 2(ab+bc+ca)$ . $9M_1^2 = 3M_2 + 2(ab+bc+ca) \Rightarrow ab+bc+ca = (9M_1^2 - 3M_2) / 2$ . Mean = $(ab+bc+ca) / 3 = (3M_1^2 - M_2) / 2$ .

MEDIUM

Mean deviation is least from [LDC-11.01.2014]

Extreme value

Mode

Median

Mean

Explanation

Mean deviation is minimal when taken from the median.

MEDIUM

The mode of the data 15, 14, 19, 20, 14, 15, 16, 14, 15, 18, 14, 19, 15, 17, 15 is- [III Grade (Maths-Science)-25.02.2023]

Explanation

Ascending order: 14, 14, 14, 14, 15, 15, 15, 15, 15, 16, 17, 18, 19, 19, 20. Frequency of 15 is maximum. Hence mode = 15.

प्राध्यापक (स्कूल शिक्षा) - 2014

MEDIUM

If the mean and median of a frequency distribution are 30 and 28 respectively, then the mode is:

Explanation

Formula: Mode = 3(Median) - 2(Mean) = 3(28) - 2(30) = 84 - 60 = 24.

MEDIUM

If the mean of observations x, x + 3, x + 5, x + 7, x + 10 is 9, then the mean of the last three observations is- [I Grade Teacher (GK) - 11.10.2022]

11 2/3

12 1/3

11 1/3

12 2/3

Explanation

Total sum = 5x + 25 = 5 * 9 = 45 => 5x = 20 => x = 4. Observations are: 4, 7, 9, 11, 14. Last three: 9, 11, 14. Mean = (9+11+14)/3 = 34/3 = 11 1/3.

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School Lecturer - 15.12.2020

MEDIUM

Find the mode of the following frequency distribution-

Class	Frequency
0-7	19
7-14	25
14-21	36
21-28	72
28-35	51
35-42	43
42-49	28

25.42

26.79

Explanation

Mode = $l + \frac{F_1-F_0}{2F_1-F_0-F_2} \times h$ . Here $l=21, F_1=72, F_0=36, F_2=51, h=7$ . Mode = $21 + \frac{72-36}{2(72)-36-51} \times 7 = 21 + \frac{36 \times 7}{57} = 21 + 4.42 = 25.42$

Head Master-2.9.2018

MEDIUM

Out of 250 observations, the mean of the first 100 observations is 5 and the mean of the remaining 150 observations is $\frac{25}{3}$ . What is the mean of the entire group of observations?

Explanation

Total sum = $100 \times 5 + 150 \times (25/3) = 500 + 1250 = 1750$ . Mean = $1750 / 250 = 7$ .

MEDIUM

The mode value of a series is- [REET(L-II)-24.7.2022(S-11)]

Intermediate value

Value with maximum frequency

Value with minimum frequency

Marginal value

Explanation

The value of the variable with the highest frequency is called the mode.

Head Master - 11.10.2021

MEDIUM

For a symmetric distribution, Mode - Median = ?

Mean

3(Mean+Median)

Explanation

In a symmetric distribution, Mean = Median = Mode. Therefore, Mode - Median = 0.

कनिष्ठ लेखाकार-04.10.2016

MEDIUM

For which value of $x$ is the mode of the following data 27? 25, 26, 27, 23, 26, 24, $x$ , 27, 26, 25, 25, 27

Explanation

Arranging data: 23, 24, 25 (3 times), 26 (3 times), 27 (3 times). For the mode to be 27, the frequency of 27 must be greater than others, so $x=27$ .

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MEDIUM

The main objective of tabulation is- [REET-24.7.2022(S-11)]

Presenting data based on their characteristics.

Presenting data in an organized manner.

Presenting complex facts in a simple form.

All of these

Explanation

All of these are objectives of tabulation.

I Grade (School Edu.)-20.10.2022

MEDIUM

If the difference between the mode and median of a data set is 24, then the difference between the median and mean is equal to-

Explanation

Formula: Mode = 3 Median - 2 Mean. Thus, Mode - Median = 2(Median - Mean). Given: Mode - Median = 24. Then 24 = 2(Median - Mean) => Median - Mean = 12. (Note: The answer provided in the book is 16, which appears to be erroneous).

प्राध्यापक (स्कूल शिक्षा) - 2012

MEDIUM

The median of the following scores of 10 students in an exam is: 22, 26, 14, 30, 18, 11, 35, 41, 12, 32

None of the above

Explanation

Ascending order: 11, 12, 14, 18, 22, 26, 30, 32, 35, 41 (Total 10 terms). Median = (5th term + 6th term) / 2 = (22+26)/2 = 48/2 = 24.

Evaluation Officer-23.08.2020

MEDIUM

The average height of a group of students is given as 67.45 inches. In the incomplete distribution of heights of 100 students, find the value of missing frequencies $f_1$ and $f_4$ -

Height (in inches)	60-62	63-65	66-68	69-71	72-74
No. of students	5	18	$f_1$	$f_4$	8

f_1=20, f_4=49

f_1=27, f_4=42

f_1=42, f_4=27

f_1=49, f_4=20

Explanation

Total $\sum f_i = 100$ . $5 + 18 + f_1 + f_4 + 8 = 100 \Rightarrow f_1 + f_4 = 69$ . Using the mean formula and solving the equations, we get $f_3 (f_1) = 42$ and $f_4 = 27$ .

CET-11.02.2023(S-II)

MEDIUM

The median of the first 10 prime numbers is-

Explanation

Prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 (Ascending order). Median = (11+13)/2 = 12

RPSC LDC-23.10.2016

MEDIUM

If the mean and median of a frequency distribution are 55.60 and 52.40 respectively, then what will be the mode of the distribution?

Explanation

Mode = 3(median) - 2(mean) = 3(52.40) - 2(55.60) = 157.2 - 111.2 = 46.

MEDIUM

Which of the following is not a source of secondary data? [REET (L-II)-24.7.2022(S-1)]

Journals

Government Reports

Survey conducted by individual personally

Data collected on the internet

Explanation

A survey conducted by an individual is a source of 'Primary data', not secondary.

Protection Officer-28.01.2023

MEDIUM

If 30 and 20 observations have been taken in two groups whose arithmetic means are 50 and 60 respectively, then the combined arithmetic mean of both the groups is-

Explanation

Combined Mean = (n1x1 + n2x2) / (n1+n2) = (3050 + 2060) / (30+20) = (1500+1200)/50 = 2700/50 = 54

RPSC LDC-19.08.2018

MEDIUM

The algebraic sum of the deviations of a set of $n$ values from their mean is-

n+1

n

n-1

Explanation

Statistical property: $\sum (x_i - \bar{x}) = 0$ . The algebraic sum of deviations from the mean is always zero.

कनिष्ठ लेखाकार-03.01.2013

MEDIUM

If in a moderately skewed distribution, the values of mode and mean are $6\lambda$ and $9\lambda$ respectively, then what will be the value of the median?

8\lambda

7\lambda

5.5\lambda

15\lambda

Explanation

Formula: $\text{Mode} = 3\text{Median} - 2\text{Mean}$ . $6\lambda = 3\text{Median} - 2(9\lambda) \implies 6\lambda = 3\text{Median} - 18\lambda \implies 24\lambda = 3\text{Median} \implies \text{Median} = 8\lambda$ .

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