Statistics Test

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Statistics Test - 23

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Weekly Quiz Competition

Question 1
1 / -0

For the measures of central tendency, ................ of the following is not true.

A
$$Z = 3M - 2 \overline x$$

B
$$2 \overline x + Z = -3M$$

C
$$2 \overline x - 3M = - Z$$

D
$$2 \overline x = Z - 3M$$
Question 2
1 / -0

The modal class of the following frequency distribution is ............
Class 0-10 10-20 20-30 30-40 40-50
Frequency $$7$$ $$15$$ $$13$$ $$17$$ $$10$$

A
$$20-30$$

B
$$10-20$$

C
$$30-40$$

D
$$40-50$$

Solution

From the table, the largest frequency is $$17$$ which the frequency of class $$30-40$$.
The class having highest frequency is the modal class.
Hence the modal class is $$30-40$$.
Question 3
1 / -0

The mode of the following distribution is __________.
Size $$2$$ $$3$$ $$4$$ $$5$$ $$6$$ $$7$$ $$8$$
Frequency $$10$$ $$12$$ $$25$$ $$20$$ $$25$$ $$15$$ $$11$$

A
Only $$4$$

B
Only $$6$$

C
Both $$4$$ and $$6$$

D
$$5$$

Solution

Mode of a data is the quantity which occurs the most or has highest frequency.

In the given data both $$4$$ and $$6$$ have $$25$$ frequency and is the highest.

$$\therefore$$ Mode are both $$4$$ and $$6$$
Question 4
1 / -0

The mode from the following table will be:
Term $$25$$ $$35$$ $$45$$ $$55$$ $$65$$
Frequency $$14$$ $$16$$ $$24$$ $$20$$ $$6$$

A
$$24$$

B
$$45$$

C
$$65$$

D
$$6$$

Solution

Mode is the data point with maximum occurrence.
From the given data we can see that $$45$$ is repeated $$24$$ times, which is maximum.
Hence the mode of the given data is $$45$$.
Question 5
1 / -0

Size 2 3 4 5 6 7 8
Frequency 10 12 25 20 25 15 11
The mode of the following distribution is ______.

A
$$2$$

B
$$8$$

C
Both $$4$$ and $$6$$

D
$$5$$

Solution

Mode is that observation which have highest frequency. Since, both $$4$$ and $$6$$ have highest frequency i.e. $$25$$ and $$25$$, they are the mode of the given distribution.
Hence, option (C) is correct.
Question 6
1 / -0

The relation between mean, median and mode is __________.

A
$$Mode = 3(Median) - 2(Mean)$$

B
$$Mode = 2(Median) - 3(Mean)$$

C
$$Mode = 3(Mean) - 2(Median)$$

D
$$Mode = 2(Mean) - 3(Median)$$

Solution

An empirical relation exists in between mean, median and mode which is
Mode $$= 3 ($$Median$$) - 2($$Mean$$)$$
Question 7
1 / -0

Compute mode of the following distribution:
$$\chi$$ $$10$$ $$11$$ $$12$$ $$13$$ $$14$$ $$15$$ $$16$$ $$17$$ $$18$$ $$19$$
$$f$$ $$8$$ $$15$$ $$20$$ $$100$$ $$98$$ $$95$$ $$90$$ $$75$$ $$50$$ $$30$$

A
$$15.09$$

B
$$5$$

C
$$13$$

D
$$15$$

Solution

Since, corresponding to the value of x =13 we have maximum frequency.
So, mode is 13.
Question 8
1 / -0

For a frequency distribution, mean, median and mode are connected by which of the following relations?

A
Mode $$=3$$ Mean $$-2$$ Median

B
Mode $$=2$$ Median $$-3$$ Mean

C
Mode $$=3$$ Median $$-2$$ Mean

D
Mode $$=3$$ Median $$+2$$ Mean

Solution

Mode $$=$$ $$3$$ Median $$-$$ $$2$$ Mean is an empirical formula which holds true when the distribution is uniform.

This is an approximate relation that holds when the distribution is symmetrical or moderately skewed. It does not hold when the distribution is too skewed. When the distribution is symmetric, this relation holds exactly because in that case, mean=median=mode.

The figures show how this relation works.
Question 9
1 / -0

Which of the following is not a measure of central tendency?

A
Mean

B
Median

C
Mode

D
None of above

Solution

$${\textbf{Step -1: Defining all terms}}$$
$$\text{Mean is the average }$$

$${\text{Median is the middle number,when data is arranged in numerical order}}{\text{.}}$$

$${\text{Mode is the data item that appears most frequently}}{\text{.}}$$

$${\textbf{Hence, mean, median and mode are all measures of central tendencies}}{\text{.}}$$$$\textbf{Therefore, correct answer is option D.}$$
Question 10
1 / -0

For the given table, the mode mark is
Mark 3 4 5 6 8 9 10 11
Frequency 8 4 9 8 6 10 9 7

A
$$6$$

B
$$3$$

C
$$9$$

D
$$7$$

Solution

Mode is the value which is most frequent, i.e, maximum frequency.
So, maximum frequency is 10 for 9 mark.
Hence, mode mark is 9.

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Re-Attempt Weekly Quiz Competition

Class	0-10	10-20	20-30	30-40	40-50
Frequency	$$7$$	$$15$$	$$13$$	$$17$$	$$10$$

Size	$$2$$	$$3$$	$$4$$	$$5$$	$$6$$	$$7$$	$$8$$
Frequency	$$10$$	$$12$$	$$25$$	$$20$$	$$25$$	$$15$$	$$11$$

Term	$$25$$	$$35$$	$$45$$	$$55$$	$$65$$
Frequency	$$14$$	$$16$$	$$24$$	$$20$$	$$6$$

$$\chi$$	$$10$$	$$11$$	$$12$$	$$13$$	$$14$$	$$15$$	$$16$$	$$17$$	$$18$$	$$19$$
$$f$$	$$8$$	$$15$$	$$20$$	$$100$$	$$98$$	$$95$$	$$90$$	$$75$$	$$50$$	$$30$$

Size	2	3	4	5	6	7	8
Frequency	10	12	25	20	25	15	11

Mark	3	4	5	6	8	9	10	11
Frequency	8	4	9	8	6	10	9	7

Statistics Test - 23

Result

Statistics Test - 23

Score

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Rank

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Question 1

$$Z = 3M - 2 \overline x$$

$$2 \overline x + Z = -3M$$

$$2 \overline x - 3M = - Z$$

$$2 \overline x = Z - 3M$$

Question 2

$$20-30$$

$$10-20$$

$$30-40$$

$$40-50$$

Solution

Question 3

Only $$4$$

Only $$6$$

Both $$4$$ and $$6$$

$$5$$

Solution

Question 4

$$24$$

$$45$$

$$65$$

$$6$$

Solution

Question 5

$$2$$

$$8$$

Both $$4$$ and $$6$$

$$5$$

Solution

Question 6

$$Mode = 3(Median) - 2(Mean)$$

$$Mode = 2(Median) - 3(Mean)$$

$$Mode = 3(Mean) - 2(Median)$$

$$Mode = 2(Mean) - 3(Median)$$

Solution

Question 7

$$15.09$$

$$5$$

$$13$$

$$15$$

Solution

Question 8

Mode $$=3$$ Mean $$-2$$ Median

Mode $$=2$$ Median $$-3$$ Mean

Mode $$=3$$ Median $$-2$$ Mean

Mode $$=3$$ Median $$+2$$ Mean

Solution

Question 9

Mean

Median

Mode

None of above

Solution

Question 10

$$6$$

$$3$$

$$9$$

$$7$$

Solution

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