Properties of Measures of Central Tendency

Q.

In a test called ACSAT, the average marks of $15$ test takers are $240$. if the marks of $5$ test takers are subtracted, the average marks decrease by $40$. what are the average marks of $5$ test takers?

Q.

Assume there are four families in a country. The average per capita income of these families is $\text{Rs}5000$. If the income of three families is $\text{Rs}4000$, $\text{Rs}7000$ and $\text{Rs}3000$ respectively, what is the income of the fourth family?

1. $\text{Rs 7500}$

2. $\text{Rs 3000}$

3. $\text{Rs 2000}$

4. $\text{Rs 6000}$

Q.

In a camp, there is enough flour for 300 persons for 42 days. How long will the flour last, if 20 more persons join the camp?

Q. Question 11
Consider the following distribution
$\begin{array}{cc}Marksobtained& Numberofstudents\\ Morethanorequalto0& 63\\ Morethanorequalto10& 58\\ Morethanorequalto20& 55\\ Morethanorequalto30& 51\\ Morethanorequalto40& 48\\ Morethanorequalto50& 42\end{array}$
the frequency of the class 30-40 is
(a) 3
(b) 4
(c) 48
(d) 51

Q.

Question 15

One packet of biscuits requires $2\frac{1}{2}$ cups of flour and $1\frac{2}{3}$ cups of sugar. The estimated total quantity of both ingredients used in 10 such packets of biscuits will be

Q.

Calculate the mean of the scores of $20$ students in a mathematics test : Marks $10-20,20-30,30-40,40-50,50-60$ . Number of students $2,4,7,6,1$

Q. The algebraic sum of the deviations of a frequency distribution from its mean is ____.

1. always positive
2. zero
3. always negative
4. non – zero number

Q.

Coefficient of variation can be defined as C.V = $\frac{\sigma }{x}\times 100$, $\overline{x}$ $\ne$ 0, $\sigma$ = standard deviation and $\overline{x}$ = mean

1. True

2. False

Q.

If the variable takes the values $0,1,2,...,n$ with frequencies proportional to the binomial coefficients $C\left(n,0\right),C\left(n,1\right),C\left(n,2\right),...,C\left(n,n\right)$respectively, then the variance of the distribution is

1. $n$

2. $\frac{\sqrt{n}}{2}$

3. $\frac{n}{2}$

4. $\frac{n}{4}$

Q. Question 7
In the class intervals, 10 - 20, 20 - 30, the number 20 is included in:

A) 10 - 20
B) 20 - 30
C) Both the intervals
D) None of these

Q.

The class mark of the class $100-120$ is:

1. $100$

2. $115$

3. $110$

4. $120$

Q.

What do you call the most frequent observation in the data?

__

Q.

Find the mean salary of $60$ workers of a factory from the following table:

Salary in Rupees	Number of workers
$3000$	$16$
$4000$	$12$
$5000$	$10$
$6000$	$8$
$7000$	$6$
$8000$	$4$
$9000$	$3$
$10000$	$1$
Total	$60$

Q.

The shadow of a 3m long stick is 4m long. At the same time of the day, if the shadow of a flagstaff is 24 long, how tall is the flagstaff?

Q.

Find: $14.49÷7$

Q.

Question 92

There are 20 grams of protein in 75 grams of sauted fish. How many grams fo protein is in 225 grams of that fish?

Q.

How harmonic mean is different from arithmetic mean?

Q.

If the mean and variance of a Binomial variate $X$ are $8$ and $4$ respectively, then $P(X<3)$ equals

1. $\frac{265}{2^{15}}$

2. $\frac{137}{2^{14}}$

3. $\frac{137}{2^{16}}$

4. $\frac{265}{2^{16}}$

Q.

A runner covers a distance of $270metres$ in $30seconds$.

Find his speed in $m/s$

Q.

Is The Sum Of Deviations Always Zero?

1. True
2. False

Q.

The average age of 29 boys of a class is 17 years . When the age of the class teacher is included , the average age becomes 18 years . Find the age of the class teacher.

Q.

In a class test, if the marks scored by 11 students are 13, 17, 20, 5, 3, 19, 7, 6, 11, 15 and 17. Then, match the following:
$\begin{array}{cccc}& ListI& & ListII\\ A.& Median& i& 17\\ B.& Lowerquartile& ii.& 11\\ C.& Upperquartile& iii.& 6\\ D.& Interquartilerange& iv.& 13\end{array}$

1. A-i, B-ii, C-iii, D-iv

2. A-ii, B-iv, C-iii, D-i

3. A-iv, B-iii, C-ii, D-i

4. A-iv, B-iii, C-i, D-ii

Q.

Write the class marks of the class interval $30-40$.

Q.

Is harmonic mean greater than arithmetic mean?

Q.

The mean weight of 8 students is 45.5 kilogram 2 more students having weight of 41.7 kg and 53.3 kg join the group what is the new mean weight

Q.

If AM of two numbers is twice of their GM, then the ratio of greatest number to smallest number is

1. $7-4\sqrt{3}$

2. $7+4\sqrt{3}$

3. $21$

4. $5$

Q.

If $a,b$ and $c$ are non-coplanar, then the value of $\frac{1}{3}\left[\frac{a·(b\times c)}{b·(c\times a)}\right]-\frac{1}{2}\left[\frac{b·(c\times a)}{c·(a\times b)}\right]$ is?

1. $-\frac{1}{2}$

2. $-\frac{1}{3}$

3. $-\frac{1}{6}$

4. $\frac{1}{6}$

Q. Question 18
The mean of 100 observations is 50. If one of the observations which was 50 is replaced by 150, the resulting mean will be:

A) 50.5
B) 51
C) 51.5
D) 52

Q. Question 4 (iv)
Express in Kg
2598mg

Q.

Question 07.1.
Suppose 2 kg of sugar contains $9\times {10}^6$ crystals. How many sugar crystals are there in 5 kg of sugar?