Statistics Test

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Statistics Test - 25

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Weekly Quiz Competition

Question 1
1 / -0

Median is based on the...

A
highest $$50$$ $$\%$$ of items

B
lowest $$25$$ $$\%$$ of items

C
highest $$25$$ $$\%$$ of items

D
middle $$50$$ $$\%$$ of items

Solution

Median, by definition is the term that
occurs in the middle. Hence it depends upon
the middle 50% of the given items.
Question 2
1 / -0

The mode of the distribution
Marks 4 5 6 7 8
No. of students 6 7 10 8 3

A
5

B
6

C
8

D
10

Solution

$$\Rightarrow$$ Mode is a number which occurs maximum number of times.
$$\Rightarrow$$ Here, in given frequency table we can see, maximum marks obtained by students is $$6$$
$$\therefore$$ $$Mode=6$$
Question 3
1 / -0

If in a frequency distribution the mean and median are $$25$$ and $$26$$ then its mode is ________

A
$$27$$

B
$$28$$

C
$$29$$

D
$$32$$

Solution

As we know that,
$$\text{Mode} = 3 \text{ Median} - 2 \text{ Mean}$$
Given:-
Mean $$= 25$$
Median $$= 26$$
Therefore,
Mode $$= 3 \times 26 - 2 \times 25 \\ = 78 - 50 = 28$$
Question 4
1 / -0

The lower limit of the modal class of the following data is:
Class interval
$$5 - 10$$
$$10 - 15$$
$$15 - 20$$
$$20 - 25$$
$$25 - 30$$
$$30 - 35$$
Frequency
$$5$$
$$15$$
$$6$$
$$10$$
$$14$$
$$9$$

A
$$25$$

B
$$15$$

C
$$10$$

D
$$30$$

Solution

Modal class is the class that has the highest frequency.
The highest frequency in the table is $$15$$ which occurs in the interval $$10-15$$.
The lower limit is the smallest in the class interval.
Therefore, the lower limit in the class interval $$10-15$$ is $$10$$.
Question 5
1 / -0

The lower limit of the modal class of the following data is :
C. I.
0 - 10
10 - 20
20 - 30
30 - 40
40 - 50
Frequency
5
8
13
7
6

A
10

B
30

C
20

D
50

Solution

Modal is the class which has the highest frequency.
Therefore, the highest frequency is $$13$$ which occurs in the interval $$20-30$$
Lower limit of the class is the smallest value of the class.
Therefore, the lower limit of the class $$20-30$$ is $$20$$
Question 6
1 / -0

The mean of $$25$$ observations is $$36$$. Out of these observations if the mean of first $$13$$ observations is $$32$$ and that of the last $$13$$ observations is $$40$$, the $$13$$th observation is :

A
$$23$$

B
$$36$$

C
$$38$$

D
$$40$$
Solution
Mean of $$25$$ observations =$$ 36$$
Sum of $$25$$ observations = $$36\times25 = 900$$
Mean of first $$13$$ observations= $$32$$
Sum of first $$13$$ observations = $$32\times13 = 416$$
Mean of Last $$13$$ observation=$$40$$
Sum of Last 13 observations = $$40\times13$$ = $$520$$

Sum of first$$13$$ observation+ Sum of last$$13$$ obs $$-$$ $$13$$th observation$$=$$ Total sum of $$25$$ observations
$$416 +520 - 13th\ observation = 900$$
- $$13$$ th observation $$ =36$$
Question 7
1 / -0

In a moderately skewed distribution the values of mean and median are $$4$$ and $$5$$ respectively. The value of mode is approx.

A
$$4$$

B
$$5$$

C
$$6$$

D
$$7$$

Solution

Mode = $$3\times$$ median $$- 2\times$$ mean
$$=3 \times 5 - 2 \times 4$$
$$= 1 5 - 8 = 7$$
Hence, option 'D' is correct.
Question 8
1 / -0

The abscissa of the point of intersection of the less than type and of the more than type cumulative frequency curves of a grouped data gives its:

A
mean

B
median

C
mode

D
all the three above

Solution

The ogive is the free hand graph.
The abscissa (X-coordinate) of the intersection of the less than ogive and more than ogive gives the median of the data.
In the above graph, the intersection point is $$(15,40)$$. The X-coordinate $$15$$ is the median.
Question 9
1 / -0

The median of the following data is :

A
30

B
40

C
35

D
31

Solution

Number of $$x$$ values is $$2+3+2+3+1=11$$ (odd number).
Since, the total values are odd. There the median occurs at the $$\dfrac{n+1}2=\left(\dfrac{11+1}{2}\right)^{th}=6^{th}$$ position.
The position is calculated by adding the frequencies.

$$x:$$ 10 20 30 40 50
$$f:$$ 2 3 2 3 1
position 2 2+3=5 5+2=7 7+3=10 10+1=11
$$6^{th}$$ position is after $$5^{th}$$ position and before $$7^{th}$$. Therefore the median is $$30$$.
Question 10
1 / -0

The relation connecting the measures of central tendencies is :

A
$$mode = 2 median - 3 mean$$

B
$$mode = 3 median - 2 mean$$

C
$$mode = 2 median + 3 mean$$

D
$$mode = 3 median + 2 mean$$

Solution

In statistics, central tendency is the central value for a probability distribution.

The most common measures of central tendencies are mean, median and mode.

The relation between mean median and mode is given by the empirical formula $$mode=3median-2mean$$

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Class interval	$$5 - 10$$	$$10 - 15$$	$$15 - 20$$	$$20 - 25$$	$$25 - 30$$	$$30 - 35$$
Frequency	$$5$$	$$15$$	$$6$$	$$10$$	$$14$$	$$9$$

Marks	4	5	6	7	8
No. of students	6	7	10	8	3

$$x:$$	10	20	30	40	50
$$f:$$	2	3	2	3	1
position	2	2+3=5	5+2=7	7+3=10	10+1=11

Statistics Test - 25

Result

Statistics Test - 25

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SHARING IS CARING

Question 1

highest $$50$$ $$\%$$ of items

lowest $$25$$ $$\%$$ of items

highest $$25$$ $$\%$$ of items

middle $$50$$ $$\%$$ of items

Solution

Question 2

5

6

8

10

Solution

Question 3

$$27$$

$$28$$

$$29$$

$$32$$

Solution

Question 4

$$25$$

$$15$$

$$10$$

$$30$$

Solution

Question 5

10

30

20

50

Solution

Question 6

$$23$$

$$36$$

$$38$$

$$40$$

Solution

Question 7

$$4$$

$$5$$

$$6$$

$$7$$

Solution

Question 8

mean

median

mode

all the three above

Solution

Question 9

30

40

35

31

Solution

Question 10

$$mode = 2 median - 3 mean$$

$$mode = 3 median - 2 mean$$

$$mode = 2 median + 3 mean$$

$$mode = 3 median + 2 mean$$

Solution

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