Statistics Test

Result

Statistics Test - 15

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Weekly Quiz Competition

Question 1
1 / -0

$$2(Median - Mean )=Mode -Mean$$

A
True

B
False

C
Neither

D
Either

Solution

$$ 2(Median - Mean) = Mode - Mean$$

$$2(Median) = Mode + Mean$$

This essentially means that the statement is saying that the Median is the average of Mode and Mean in the given data, which is not correct.
Question 2
1 / -0

Value of the middle-most observation(s) is called:

A
Mean

B
Median

C
Mode

D
None of these

Solution

To find the Median, place the numbers in value order and find the middle number.
If there are two middle numbers, take the mean of the two numbers and this will be the median of the data set.
The middle most observation of a data series is called the median of the series.
Question 3
1 / -0

Formula to find mode is

A
Mean - 2 Median

B
3 Median - 2 Mean

C
3 Median - Mean

D
Mean + Median

Solution

Mode can be found by using the formula:

Mode = 3 Median - 2 Mean
Question 4
1 / -0

Mode of $$2, 3, 4, 5, 0, 1, 3, 3, 4, 3\ is\ 3.$$

A
True

B
False

C
Neither

D
None

Solution

Mode is the term which appears maximum number of times.

The terms are: 2, 3, 4, 5, 0, 1, 3, 3, 4, 3
Arranging them in ascending order: 0,1,2,3,3,3,3,4,4,5
3 is occurring maximum number of times. hence mode is 3.
Question 5
1 / -0

STATEMENT -1 : Histogram is useful to determine graphically the value of mode.
STATEMENT -2 : The empirical relationship between average, median and mode is mode $$=$$ $$3$$ median $$- 2$$ mean.

A
Statement - 1 is True, Statement - 2 is True, Statement - 2 is a correct explanation for Statement - 1

B
Statement - 1 is True, Statement - 2 is True : Statement 2 is NOT a correct explanation for Statement - 1

C
Statement - 1 is True, Statement - 2 is False

D
Statement - 1 is False, Statement - 2 is True

Solution

Statement - 1 is True, Statement - 2 is True : Statement 2 is NOT a correct explanation for Statement - 1.
Reason :-
Empherical relationship between average, median, mode helps to find the other value using two of the values while Statement - 1 i.e. Histogram is use to graphically determine the value of mode only. Thus, Statement - 2 does not explain and relate to Statement - 1.
Question 6
1 / -0

A student got marks in $$5$$ subjects in a monthly test is given below: $$2, 3, 4, 5, 6$$.
In these obtained marks, $$4$$ is the

A
Mean and median

B
Median but no mean

C
Mean but no median

D
Mode

Solution

Marks obtained $$= 2,3,4,5,6$$

Median is the middle term $$= 4$$.
Mean $$= \dfrac{2+3+4+5+6}{5} = 4$$.
Question 7
1 / -0

What is the mode from the following table ?
Marks obtained
Frequency
3
1
23
33
43
7
11
15
8
3

A
$$13$$

B
$$43$$

C
$$33$$

D
$$23$$

Solution

Mode is the value which has the highest frequency.
In the given table, $$23$$ has the highest frequency $$15$$ i.e., $$23 $$ marks were obtained to many people than other marks.
Therefore $$23$$ is the mode.
Question 8
1 / -0

One of the method of determining mode is

A
Mode = 2Median - 3Mean

B
Mode = 2 Median + 3 Mean

C
Mode = 3 Median - 2 Mean

D
Mode = 3 Median + 2 Mean

Solution

It is well known fact that for moderately skewed matrix :
Mode $$=3$$ Median $$-2$$ Mean
Question 9
1 / -0

The marks of $$20$$ students in a test were as follows:
$$5, 6, 8, 9, 10, 11, 11, 12, 13, 13, 14, 14, 15, 15, 15, 16, 16, 18, 19, 20$$
The mode is

A
$$20$$

B
$$10$$

C
$$15$$

D
$$25$$

Solution

Terms are: $$5, 6, 8, 9, 10, 11, 11, 12, 13, 13, 14, 14, 15, 15, 15, 16, 16, 18, 19, 20$$.
$$15$$ occurs most number of times $$(3$$ times$$)$$.
Hence, $$15$$ is the mode of the marks.
Question 10
1 / -0

Calculate the mode for $$17, 12, 19, 11, 20, 11, 20, 19, 10, 25,19$$.

A
$$12$$

B
$$17$$

C
$$19$$

D
$$25$$

Solution

Mode is the value which occurs most often in the data set of values.
Given data set is $$17,12,19,11,20,11,20,19,10,25,19$$
In the above data set, value $$19$$ has occurred many times i.e., 3 times.
Therefore the mode of the given data set is $$19$$

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Marks obtained	Frequency
3 1 23 33 43	7 11 15 8 3

Statistics Test - 15

Result

Statistics Test - 15

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Rank

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SHARING IS CARING

Question 1

True

False

Neither

Either

Solution

Question 2

Mean

Median

Mode

None of these

Solution

Question 3

Mean - 2 Median

3 Median - 2 Mean

3 Median - Mean

Mean + Median

Solution

Question 4

True

False

Neither

None

Solution

Question 5

Statement - 1 is True, Statement - 2 is True, Statement - 2 is a correct explanation for Statement - 1

Statement - 1 is True, Statement - 2 is True : Statement 2 is NOT a correct explanation for Statement - 1

Statement - 1 is True, Statement - 2 is False

Statement - 1 is False, Statement - 2 is True

Solution

Question 6

Mean and median

Median but no mean

Mean but no median

Mode

Solution

Question 7

$$13$$

$$43$$

$$33$$

$$23$$

Solution

Question 8

Mode = 2Median - 3Mean

Mode = 2 Median + 3 Mean

Mode = 3 Median - 2 Mean

Mode = 3 Median + 2 Mean

Solution

Question 9

$$20$$

$$10$$

$$15$$

$$25$$

Solution

Question 10

$$12$$

$$17$$

$$19$$

$$25$$

Solution

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