Measures of Central Tendency Test

Result

Measures of Central Tendency Test - 16

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Weekly Quiz Competition

Question 1
1 / -0

The median of the following data $$36, 74, 77, 31, 68, 76, 34, 80, 64, 32, 82$$ is-

A
$$68$$

B
$$34$$

C
$$67$$

D
$$76$$

Solution

Arrange the given data in ascending order we have,
$$31, 32, 34, 36, 64, 68, 74, 76, 77, 80$$ and $$82$$
Median $$=\cfrac{N+1}{2}=\cfrac{11+1}{2}=\cfrac{12}{2}=6$$
The sixth entry is $$68$$
Median is $$68$$
Question 2
1 / -0

The arithmetic mean of first five natural number is

A
$$2$$

B
$$3$$

C
$$4$$

D
$$8$$

Solution

Formula used:
$$\text{Arithmetic mean}= \dfrac{\text{Sum of given numbers}}{\text{Total numbers}}$$

Apply the above formula, we get
$$\text{Arithmetic mean}=\cfrac{1+2+3+4+5}{5}$$
$$=3$$
Question 3
1 / -0

The median of 9, 5, 7, 11, 13, 3 is

A
8

B
9

C
7

D
11

Solution

Arranging data in ascending order: 3, 5, 7, 9, 11, 13
Middle terms: 7, 9
Median=$$\displaystyle \frac{7+9}{2}=8$$
Question 4
1 / -0

The weight (in kg) of $$7$$ women are $$40, 64, 65, 30, 80, 67$$ and $$70$$. The median is-

A
$$80$$ kg

B
$$30$$ kg

C
$$65$$ kg

D
$$70$$ kg

Solution

Arranging in the ascending order we have
$$30, 40, 64, 65, 67, 70, 80$$
Hence median $$=65$$
Question 5
1 / -0

A candidate obtained the following percentage of marks in an examination English 60, Maths 90, Physics 75, Chemistry 66. If weighs 2, 4, 3, 3 are allotted to these subjects respectively then the weight mean is given by

A
$$\displaystyle \frac{60+90+75+66}{2+4+3+3}$$

B
$$\displaystyle \frac{60\times 2+90\times 4+75\times 3+66\times 3}{2+4+3+3}$$

C
$$\displaystyle \frac{60\times 2+90\times 4+75\times 3+66\times 3}{4}$$

D
$$\displaystyle \frac{60+90+75+66}{4}$$

Solution

A candidate obtained the following percentage of marks in an examination English 60, Maths 90, Physics 75, Chemistry 66. If weighs 2, 4, 3, 3 are allotted to these subjects
Then total number English =$$60\times 2$$
And  total number Maths =$$90\times 4$$
And  total number Physics =$$75\times 3$$
And  total number Chemistry =$$66\times 3$$
So weight of subjects mean =$$\frac{60\times 2+90\times 4+75\times 3+66\times 3}{2+4+3+3}$$
Question 6
1 / -0

The value of $$\displaystyle \sum ^{n}_{i=1}\left ( x_{1} -\bar{x}\right )$$ where $$\displaystyle \bar{x}$$ is the arith metic mean of $$\displaystyle x_{i}$$ is

A
1

B
0

C
$$\displaystyle n\bar{x}$$

D
none of these

Solution

The $$\bar{x}=\frac{x_{1}}{1}$$
Then $$\sum_{i=1}^{n}(x_{1}-\bar{x})=\bar{x}-\bar{x}=0$$
Question 7
1 / -0

The daily earnings (in rupees) of $$10$$ workers in a factory are $$6, 14, 17, 6, 14, 17, 14, 6, 17, 14$$.
The median wage is-

A
Rs.$$6$$

B
Rs.$$14$$

C
Rs.$$15$$

D
Rs.$$17$$

Solution

Arranging the daily earnings in ascending order, we have
$$6, 6, 6, 14, 14, 14, 14, 17, 17, 17$$ the median is average of 5th and 6th
wages i.e., $$\cfrac{14+14}{2}=14$$
Question 8
1 / -0

In the data set below, what is the upper quartile?
$$1, 2, 4, 2, 5, 6, 7$$

A
$$2$$

B
$$7$$

C
$$6$$

D
$$4$$

Solution

First arrange the data set in order.
$$1, 2, 2, 4, 5, 6, 7$$
Here the median is the middle number $$= 4$$
So, the upper quartile is the median of the higher half of the data.
Then, the middle of the upper half will be $$5, 6, 7$$
Therefore, the upper quartile is $$6$$.
Question 9
1 / -0

In the data set below, what is the lower quartile?
$$1, 2, 4, 2, 5, 6, 7$$

A
$$1$$

B
$$2$$

C
$$4$$

D
$$5$$

Solution

First arrange the data set in order.
$$1, 2, 2, 4, 5, 6, 7$$
Here the median is the middle number $$= 4$$
So, the lower quartile is the median of the lower half of the data.
Then, the middle of the lower half will be $$1, 2, 2$$
Therefore, the lower quartile is $$2$$.
Question 10
1 / -0

From the following data$$: 7, 3, 4, 5, 7, 7, 7, 3, 2, 1, 8, 2.$$ Find the mode.

A
$$3$$

B
$$7$$

C
$$2$$

D
$$5$$

Solution

Given data is $$7,3,4,5,7,7,7,3,2,1,8,2$$
The mode is the value which appears most often. In the above data the value which appears most often is $$7$$.
Since it appears $$4$$ times. So, mode is $$7$$.

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Re-Attempt Weekly Quiz Competition

Measures of Central Tendency Test - 16

Result

Measures of Central Tendency Test - 16

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SHARING IS CARING

Question 1

$$68$$

$$34$$

$$67$$

$$76$$

Solution

Question 2

$$2$$

$$3$$

$$4$$

$$8$$

Solution

Question 3

8

9

7

11

Solution

Question 4

$$80$$ kg

$$30$$ kg

$$65$$ kg

$$70$$ kg

Solution

Question 5

$$\displaystyle \frac{60+90+75+66}{2+4+3+3}$$

$$\displaystyle \frac{60\times 2+90\times 4+75\times 3+66\times 3}{2+4+3+3}$$

$$\displaystyle \frac{60\times 2+90\times 4+75\times 3+66\times 3}{4}$$

$$\displaystyle \frac{60+90+75+66}{4}$$

Solution

Question 6

1

0

$$\displaystyle n\bar{x}$$

none of these

Solution

Question 7

Rs.$$6$$

Rs.$$14$$

Rs.$$15$$

Rs.$$17$$

Solution

Question 8

$$2$$

$$7$$

$$6$$

$$4$$

Solution

Question 9

$$1$$

$$2$$

$$4$$

$$5$$

Solution

Question 10

$$3$$

$$7$$

$$2$$

$$5$$

Solution

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