Measures of Central Tendency Test

Result

Measures of Central Tendency Test - 42

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

What is the mode for the data 20, 20, 20,21, 21, 21, 21, 21, 22, 22, 22, 22, 22, 22, 22, 23, 23, 23, 23, 23, 24, 24, 25 ?

A
7

B
21

C
22

D
25

Solution

Mode is the value that appears in a given data more often than the others. If two numbers appear maximum no of times we take average of both.
So no of 20's=3
no of 21's=5
no of 22's=7
no of 23's=5
no of 24's=2
no of 25's=1
Since 22 appear more no of times, mode of given data is 22.
Question 2
1 / -0

Find the mean of the first five prime numbers.

A
3.3

B
7.8

C
5.6

D
12.1

Solution

First five prime numbers are $$2, 3, 5, 7$$ and $$11.$$
Number of observations $$=5$$
$$Mean=\dfrac{Sum\,of\,the\,numbers}{No.\,of\,observations}$$
$$=\dfrac{2+3+5+7+11}{5}$$
$$=\dfrac{28}{5}$$
$$=5.6$$
Question 3
1 / -0

The mean of the values $$0, 1, 2, ..... , n$$ having corresponding weight $$^nC_0, ^nC_1, ^nC_2, ..... , ^nC_n$$ respectively, is?

A
$$\displaystyle\frac{2^n}{(n+1)}$$

B
$$\displaystyle\frac{2^{n+1}}{n(n+1)}$$

C
$$\displaystyle\frac{n+1}{2}$$

D
$$\displaystyle\frac{n}{2}$$

Solution

The solution mean is $$\bar{x}=\displaystyle\frac{0\cdot 1+1\cdot \, ^nC_1+2\cdot \,^nC_2+3\cdot \,^nC_3+....+n\cdot \,^nC_n}{1+\,^nC_1+\,^nC_2+....+\,^nC_n}$$

$$=\frac{\displaystyle \sum_{r=0}^n\,r\cdot\, ^nC_r}{\displaystyle \sum_{r=0}^n\,^nC_r} = \frac{\displaystyle \sum_{r=1}^n \,r\cdot \frac{n}{r}\,\cdot \,^{n-1}C_{r-1}}{\displaystyle \sum_{r=0}^n\,^nC_r}$$

$$=\frac{n\displaystyle \sum_{r=1}^n\,^{n-1}C_{r-1}}{\displaystyle \sum_{r=0}^n \, ^nC_r}$$

$$=\displaystyle\frac{n\cdot 2^{n-1}}{2^n}=\frac{n}{2}$$
Question 4
1 / -0

The 'less than' ogive curve and the 'more than' ogive curve intersect at.

A
Median

B
Mode

C
Arithmetic mean

D
None of the above

Solution

The less than ogive curve gives cumulative frequency (probability) for $$x <= a.$$
The more than ogive curve gives cumulative frequency (probability) for $$x >= a.$$
They intersect exactly at the median, as cumulative frequency will be % of the total at median.
The 'less than' ogive curve and the 'more than' ogive curve intersect at Median.
Option A is correct Answer.
Question 5
1 / -0

The median of the following numbers $$25, 27, 21, 23, 24$$ is ___________.

A
$$21$$

B
$$23$$

C
$$25$$

D
$$24$$

Solution

Arranging the numbers in ascending order:
$$21,23,24,25,27$$
Median of the numbers is $$\dfrac{n+1}{2}th$$ number from starting,
where $$n$$ is the no of total numbers.
Here $$n=5$$
$$\text{median}=3^{rd}$$ term $$=24$$
Question 6
1 / -0

A variate X takes values 2, 9, 3, 7, 5, 4, 3, 2, 10. What is the median?

A
2

B
4

C
7

D
9

Solution

The data point which is in middle of ascending or descending series is called median.
So, for data $$2,9,3,7,5,4,3,2,10$$
Arranging in ascending order $$2,2,3,3,4,5,7,9,10$$
So, middle value is $$4.$$
Median of the given data set is $$4.$$
Question 7
1 / -0

Which of the following is true?

A
The arithmetic mean is affected by the presence of extreme values in the data.

B
Median is that positional value of the variable which divides the distribution into two equal parts

C
The median is not affected by the presence of extreme values in the data.

D
All of these

Solution

Arithmetic mean refers to the average amount in a given group of data. So arithmetic mean can be calculated by adding the first term and the last term of the series and then dividing it by 2. So arithmetic mean is affected by the presence of extreme values in the data.
Median is the middle most value of a given series that represents the whole class of the series.So since it is a positional average, it is calculated by observation of a series and not through the extreme values of the series which. Therefore, median is not affected by the extreme values of a series.
Question 8
1 / -0

Calculate Median value from the following frequency distribution:
X 3 5 7 9 11 13
Y(Frequency) 4 3 5 2 3 3

A
6.5

B
6

C
5.5

D
7

Solution

In order to find the median of the grouped discrete data, first we find the cumulative frequencies and the sum of frequencies.

Find the cumulative frequencies by adding the nth frequency to the sum of all the n-1 frequencies before it.
X Y (frequency) Z (Cumulative Frequency)
3 4 4
5 3 7
7 5 12
9 2 14
11 3 17
13 3 20
$$\sum{f}$$ = 4+3+5+2+3+3 =20

Since N is even, the median is:
Median = $$\dfrac{N+1}{2}$$ th term

Therefore: $$\dfrac{20+1}{2}$$ = $$\dfrac{21}{2}$$ = $$10.5$$
The Median is the average of the 10th and 11th value of the data.

Since both, the 10th and 11th term is 7, the median of the data set is 7.
Question 9
1 / -0

The mean, median and mode respectively of the numbers $$7, 4, 3, 5, 6, 3, 3, 2, 4, 3, 4, 3, 3, 4, 4, 3, 2, 2, 4, 3, 5, 4, 3, 4, 3, 4, 3, 1, 2, 3$$ are __________.

A
$$3.47, 3, 3$$

B
$$3, 3, 3$$

C
$$4, 3, 3$$

D
$$5, 4, 3$$

Solution

Sum of numbers $$=7+4+3+5+6+3+3+2+4+3+4+3+3+4+4+3+2+2+4+3$$
$$+5+4+3+4+3+4+3+1+2+3$$
$$=104$$
Total numbers are $$30$$
$$\text{mean}= \dfrac{104}{30}=3.46667=3.47$$
The mode is the number which appeared most.
Therefore, $$\text{mode}=3$$
For median arrange the numbers in ascending order:
$$1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,6,7$$
Median $$=\dfrac{(15^{th}+16^{th}) \text{term}}{2}$$
$$=\dfrac{3+3}{2}=3$$
Question 10
1 / -0

What is the class mark of the class interval-(80-90)?

A
82.5

B
90

C
80

D
85

Solution

To calculate the mean of a continuous series, mid points of the various class intervals is taken before calculating the mean which is also called the class mark. For example, if the class interval is 80-90 then before calculating the mean mid point that is the class mark is calculated which is 85.

User

Question Analysis

Correct -
Wrong -
Skipped -

My Perfomance

Score
-
out of -
Rank
-
out of -

Re-Attempt Weekly Quiz Competition

X	Y (frequency)	Z (Cumulative Frequency)
3	4	4
5	3	7
7	5	12
9	2	14
11	3	17
13	3	20

X	3	5	7	9	11	13
Y(Frequency)	4	3	5	2	3	3

Measures of Central Tendency Test - 42

Result

Measures of Central Tendency Test - 42

Score

-

Rank

-

SHARING IS CARING

Question 1

7

21

22

25

Solution

Question 2

3.3

7.8

5.6

12.1

Solution

Question 3

$$\displaystyle\frac{2^n}{(n+1)}$$

$$\displaystyle\frac{2^{n+1}}{n(n+1)}$$

$$\displaystyle\frac{n+1}{2}$$

$$\displaystyle\frac{n}{2}$$

Solution

Question 4

Median

Mode

Arithmetic mean

None of the above

Solution

Question 5

$$21$$

$$23$$

$$25$$

$$24$$

Solution

Question 6

2

4

7

9

Solution

Question 7

The arithmetic mean is affected by the presence of extreme values in the data.

Median is that positional value of the variable which divides the distribution into two equal parts

The median is not affected by the presence of extreme values in the data.

All of these

Solution

Question 8

6.5

6

5.5

7

Solution

Question 9

$$3.47, 3, 3$$

$$3, 3, 3$$

$$4, 3, 3$$

$$5, 4, 3$$

Solution

Question 10

82.5

90

80

85

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.