Measures of Central Tendency Test

Result

Measures of Central Tendency Test - 41

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
1 / -0

The average (arithmetic mean) of $$t$$ and $$y$$ is $$15$$, and the average of $$w$$ and $$x$$ is $$15$$. What is the average of $$t, w, x$$ and $$y$$?

A
$$7.5$$

B
$$15$$

C
$$22.5$$

D
$$30$$

Solution

Given, Average of $$t$$ and $$y$$ $$=$$ $$15$$
$$\Rightarrow \dfrac {t \space + \space y}{2}$$ $$=$$ $$15$$
$$\Rightarrow t$$ $$+$$ $$y$$ $$=$$ $$15$$ $$\times$$ $$2$$
$$\Rightarrow t$$ $$+$$ $$y$$ $$=$$ $$30$$

Average of$$w$$ and $$x$$ $$=$$ $$15$$
$$\Rightarrow \dfrac {w \space + \space x}{2}$$ $$=$$ $$15$$
$$\rightarrow w$$ $$+$$ $$x$$ $$=$$ $$15$$ $$\times$$ $$2$$
$$\Rightarrow w$$ $$+$$ $$x$$ $$=$$ $$30$$
Now, average of $$t$$, $$y$$, $$w$$ and $$x$$ $$=$$ $$\dfrac {(t \space + \space y \space + \space w \space + \space x)}{4}$$
$$=$$ $$\dfrac {(t \space + \space y) \space + \space (w \space + \space x)}{4}$$
$$=$$ $$\dfrac {30 \space + \space 30}{4}$$
$$=$$ $$\dfrac {60}{4}$$
$$=$$ $$15$$
Therefore, average of $$t$$, $$y$$, $$w$$ and $$x$$ is $$'15'$$.
Question 2
1 / -0

The mode of the observations $$5, 4, 4, 3, 5, x, 3, 4, 3, 5, 4, 3,$$ and $$5$$ is $$3$$. What is the median?

A
$$3$$

B
$$4$$

C
$$5$$

D
$$4.5$$

Solution

Since frequency of mode $$(3)$$ should be maximum $$x=3$$
Now, arranging data in ascending order we get
3,3,3,3,3,4,4,4,4,,5,5,5,5
Median = Middle term $$=4$$
Question 3
1 / -0

The mean of $$48, 27, 36, 24, x$$, and $$2x$$ is $$37.x =$$

A
$$13\dfrac {1}{3}$$

B
$$16\dfrac {2}{3}$$

C
$$29$$

D
$$33\dfrac {3}{4}$$

E
$$40$$

Solution

Mean $$=$$ $$\dfrac{sum \quad of \quad no.}{total \quad no}$$
$$\Rightarrow 37=\dfrac{48+27+36+24+x+2x}{6}$$
$$\Rightarrow 135+3x=222$$
$$\Rightarrow 3x=222-135$$
$$\Rightarrow 3x=87$$
$$\Rightarrow x=\dfrac{87}{3}=29$$
Question 4
1 / -0

Given, $$10, 18, 4, 15, 3, 21, x $$
If $$x$$ is the median of the $$7$$ numbers listed above, which of the following could be the value of $$x$$?

A
$$5$$

B
$$8$$

C
$$9$$

D
$$14$$

E
$$16$$

Solution

Given numbers
$$10,$$ $$18,$$ $$4,$$ $$15,$$ $$3,$$ $$21,$$ $$x$$
Median is the middle value in the list of numbers. To find the median, the numbers have to be in the numerical order.

As $$x$$ is the given median, $$x$$ should be placed in the middle of the list in numerical order. The list contains $$7$$ numbers. So, $$x$$ should be placed in the $${4}^{th}$$ position.

Rewriting the list in increasing order,
$$3,$$ $$4,$$ $$10,$$ $$x,$$ $$15,$$ $$18,$$ $$21$$

So, $$x$$ should lie between $$10$$ and $$15$$.
Possible values of $$x$$, $$10$$ $$\leq$$ $$x$$ $$\leq$$ $$15$$
From the given options,
Only $$14$$ satisfies the above condition.

Therefore, the value of $$x$$ is $$14$$.
Question 5
1 / -0

The average of six numbers is 4. If the average of two of those numbers is 2, what is the average of the other four numbers?

A
5

B
6

C
7

D
8

E
9

Solution
Question 6
1 / -0

The median of $$2, 7, 4, 8, 9, 1$$ is

A
$$4$$

B
$$6$$

C
$$5.5$$

D
$$7$$

Solution

$$1,2,4,7,8,9$$
No. of terms $$=6$$
Median $$=\dfrac{6+1}{2}=3.5$$ term
(4)th Mean = Median $$\dfrac{4+7}{2}=5.5$$
Question 7
1 / -0

For a collection of $$11$$ items, sum of all items is $$132$$, then the arithmetic mean is.

A
$$11$$

B
$$12$$

C
$$14$$

D
$$13$$

Solution
Question 8
1 / -0

The mode of the data $$5, 5, 5, 5, 5, 1, 2, 2, 3, 3, 3, 4, 4, 4, 4$$ is

A
$$2$$

B
$$3$$

C
$$4$$

D
$$5$$

Solution

$$\textbf{Step 1: Find the mode.}$$

$$\text{The given observations are : } 5, 5, 5, 5, 5, 1, 2, 2, 3, 3, 3, 4, 4, 4, 4$$

$$\text{In any series of observations, mode is the observation which appears the maximum}$$

$$\text{number of times.} $$

$$\text{Given data is 5,5,5,5,5,1,2,2,3,3,3,4,4,4,4 }$$

$$\text{In the given observations, 5 appears the maximum number of times. } $$

$$\text{So, the mode is 5.} $$

$$\textbf{Hence, the correct option is D.}$$
Question 9
1 / -0

A random sample of 20 people is classified in the following table according to their ages
Age Frequency
15-25 2
25-35 4
35-45 6
45-55 5
55-65 3
What is the mean age of this group of people?

A
$$41.0$$

B
$$41.5$$

C
$$42.0$$

D
$$42.5$$

Solution

$$Mean=\ \dfrac{\sum { (frequency\times Mid-Point)_i }}{\sum{(frequency)_i}} $$
$$Mean=\ \dfrac{830}{20}=41.5$$
Question 10
1 / -0

The following observations have been arranged in the ascending order. If the median of the data $$29, 32, 48, 50, x, x+2, 72, 78, 84, 95$$ is $$63$$, then the value of $$x$$ is ___________.

A
$$63$$

B
$$62$$

C
$$61$$

D
$$60$$

Solution

Given data is $$29, 32, 48, 50, x, x+2, 72, 78, 84, 95$$
Also given median of data $$=63$$.
Since, total number of observation are even.
So, $$\text{median}=\dfrac{x+(x+2)}{2}$$
$$=\dfrac{2x+2}{2}=x+1$$
Thus $$63=x+1$$
$$\Rightarrow x=62$$

User

Question Analysis

Correct -
Wrong -
Skipped -

My Perfomance

Score
-
out of -
Rank
-
out of -

Re-Attempt Weekly Quiz Competition

Age	Frequency
15-25	2
25-35	4
35-45	6
45-55	5
55-65	3

Measures of Central Tendency Test - 41

Result

Measures of Central Tendency Test - 41

Score

-

Rank

-

SHARING IS CARING

Question 1

$$7.5$$

$$15$$

$$22.5$$

$$30$$

Solution

Question 2

$$3$$

$$4$$

$$5$$

$$4.5$$

Solution

Question 3

$$13\dfrac {1}{3}$$

$$16\dfrac {2}{3}$$

$$29$$

$$33\dfrac {3}{4}$$

$$40$$

Solution

Question 4

$$5$$

$$8$$

$$9$$

$$14$$

$$16$$

Solution

Question 5

5

6

7

8

9

Solution

Question 6

$$4$$

$$6$$

$$5.5$$

$$7$$

Solution

Question 7

$$11$$

$$12$$

$$14$$

$$13$$

Solution

Question 8

$$2$$

$$3$$

$$4$$

$$5$$

Solution

Question 9

$$41.0$$

$$41.5$$

$$42.0$$

$$42.5$$

Solution

Question 10

$$63$$

$$62$$

$$61$$

$$60$$

Solution

User

Question Analysis

My Perfomance

Score

-

Rank

-

Results Announcement on: coming Monday

Stay Tuned: We’ll update you on your result via email or SMS.