Measures of Central Tendency Test

Result

Measures of Central Tendency Test - 29

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

Find the median of:
$$233,173,189,208,194,204,194,185,200$$ and $$220$$

A
$$194$$

B
$$185$$

C
$$197$$

D
$$220$$

Solution

Arrange the series in ascending order:
$$173, 185, 189, 194, 194, 200, 204, 208, 220, 233$$
The series has $$10$$ numbers, even numbers.
Hence, the median will be the mean of the two middle numbers
Median $$=$$ mean of $$5^{th}$$ and $$6^{th}$$ terms
Median $$= \dfrac{194 + 200}{2}$$
Median $$= 197$$
Question 2
1 / -0

Find the median of:
$$241,243,347,350,327,299,261,292,271,258$$ and $$257$$

A
$$271$$

B
$$292$$

C
$$257$$

D
$$243$$

Solution

Arrange the series in ascending order:
$$241, 243, 257, 258, 261, 271, 292, 299, 327, 347, 350$$
The series has $$11$$ terms. Hence, the median will be the middle term, i.e. $$6^{th}$$ term.
Hence, the median is $$271$$

Question 3

1 / -0

Frequency distribution of duration of $$500$$ telephone calls received at a telephone exchange on a certain day is given below :

Duration of call (in sec.)	15 - 29	30 - 44	45 - 59	60 - 74	75 - 89	90 - 104	105 - 119	120 - 134
No. of calls	8	12	61	153	190	57	10	9

Find mean duration of telephone call received at the telephone exchange.

$$74.83$$ seconds

$$79.83$$ seconds

$$83.83$$ seconds

$$86.83$$ seconds

Solution

$$ci$$	$$f_i$$	$$x_i$$	$$f_ix_i$$
14.5-29.5	8	22	176
29.5-44.5	12	37	444
44.5-59.5	61	52	3172
59.5-74.5	153	67	10251
74.5-89.5	190	82	15580
89.5-104.5	57	97	5529
104.5-119.5	10	112	1120
119.5-134.5	9	127	1143

$$N=\Sigma f_i=500$$

$$\Sigma f_ix_i=37415$$

Mean $$\overline x=\dfrac {\Sigma f_ix_i}{N}$$

$$\therefore \overline x=\dfrac{37415}{500}=74.83$$

Hence, option $$A$$ is correct.

Question 4
1 / -0

The median of $$63,17,50,9,25,43,21,50,14$$ and $$34$$ is 29.5

A
True

B
False

C
Can't determine

D
None of these

Solution

Arranging the numbers in ascending order:
$$9, 14, 17, 21, 25, 34, 43, 50, 50, 63$$
The series has $$10$$ numbers, even numbers.
Hence, the median will be the mean of the two middle numbers
Median = mean of $$5^{th}$$ and $$6^{th}$$ terms
Median = $$\frac{25 + 34}{2}$$
Median = $$29.5$$
Question 5
1 / -0

Find the arithmetic mean for the following grouped frequency distribution:
Class-intervals
$$6-10$$
$$10-14$$
$$14-18$$
$$18-22$$
$$22-26$$
$$26-30$$
Frequency
$$ 4$$
$$ 6$$
$$9$$
$$ 12$$
$$ 7 $$
$$2$$

A
$$15.8$$

B
$$16.8$$

C
$$17.8$$

D
None of these

Solution

Consider the following table, to calculate mean:
$$ci$$ $$f_i$$ $$x_i$$ $$f_ix_i$$
$$6-10$$ $$4$$ $$ 8$$ $$ 32$$
$$ 10-14$$ $$6$$ $$12$$ $$72$$
$$14-18$$ $$9$$ $$16$$ $$ 144$$
$$18-22$$ $$12$$ $$ 20$$ $$240$$
$$ 22-26$$ $$7$$ $$ 24$$ $$168$$
$$26-30$$ $$ 2$$ $$28$$ $$56$$
From the table,
$$N=\Sigma f_i=4+6+9+12+7+2=40$$

$$\Sigma f_ix_i=32+72+144+240+168+56=712$$

Mean $$\overline x=\dfrac {\Sigma f_ix_i}{N}$$
$$\therefore \overline x=\dfrac{712}{40}=17.8$$
Hence, option $$C$$ is correct.

Question 6

1 / -0

A study related to the time(in months) taken to settle a dispute in a lower court resulted the following data.

Time (in months)	$$0 - 2$$	$$2 - 4$$	$$4 - 6$$	$$6 - 8$$	$$8 - 10$$	$$10 - 12$$
No. of persons	$$15$$	$$90$$	$$120$$	$$75$$	$$70$$	$$50$$

Find the meantime taken to settle a dispute in a lower court.

$$6.9$$ months

$$6.16$$ months

$$6.66$$ months

None of these

Solution

Consider the following table to calculate mean:

Class Interval	$$f_i$$	$$x_i$$	$$f_ix_i$$
$$ 0-2$$	$$ 15$$	$$ 1$$	$$ 15$$
$$ 2-4$$	$$ 90$$	$$ 3$$	$$ 270$$
$$ 4-8$$	$$ 120$$	$$ 5$$	$$ 600$$
$$ 8-6$$	$$ 75$$	$$ 7$$	$$ 525$$
$$ 6-10$$	$$ 70$$	$$ 9$$	$$ 630$$
$$ 10-12$$	$$ 50$$	$$ 11$$	$$ 550$$

$$N=\sum f_i$$

$$=420$$

$$\sum f_ix_i=2590$$

$$\overline x=\dfrac {\sum f_ix_i}{N}$$

$$\Rightarrow \overline x=\dfrac{2590}{420}$$

$$\Rightarrow \overline x=6.16$$

The mean time to settle a dispute in a lower court is $$6.16$$ months.

Hence, option $$C$$ is correct.

Question 7
1 / -0

Median of a data set is a number which has an equal number of observations below and above it. The median of the data $$1, 9, 4, 3, 7, 6, 8, 8, 12, 15$$ is

A
$$7.5$$

B
$$7$$

C
$$8$$

D
Any number between $$7$$ and $$8$$

Solution

The data given here is: $$1, 9, 4, 3, 7, 6, 8, 8, 12, 15$$
After arranging in ascending order $$1,3,4,6,7,8,8,9,12,15$$
Since the number of terms are even, median $$= \dfrac{4^{th} + 5^{th}}{2}$$
$$= \dfrac{7 + 8}{2}$$
$$= \dfrac{15}{2}$$
$$= 7.5$$
Hence, option $$A$$ is correct.
Question 8
1 / -0

Find the median of 63, 17, 50, 9, 25, 43, 21, 50, 14 $$ and\ 34$$

A
$$29.5$$

B
$$29$$

C
$$20$$

D
$$30$$

Solution

Arranging the numbers in ascending order:
$$9, 14, 17, 21, 25, 34, 43, 50, 50, 63$$
The series has $$10$$ numbers, even numbers.
Hence, the median will be the mean of the two middle numbers
Median = mean of $$5^{th}$$ and $$6^{th}$$ terms
Median = $$\dfrac{25 + 34}{2}$$
Median = $$29.5$$
Question 9
1 / -0

The monthly salaries (in Rs.) of $$10$$ employees of a factory are: $$12000,8500,9200,7400,11300,12700,7800,11500,10320,8100$$. The median salary is:

A
Rs. $$9670$$

B
Rs. $$9760$$

C
Rs. $$6970$$

D
Rs. $$7960$$

Solution

Arranging the observation in ascending order :
$$7400, 7800, 8100, 8500, 9200, 10320, 11300, 11500, 12000, 12700$$
Total number of observations $$(n) = 10 $$
$$\displaystyle \therefore median = \frac{1}{2} \left[\left(\frac{n}{2}\right)^{th} observation + \left(\frac{n}{2} + 1 \right)^{th} observation \right]$$
$$\displaystyle = \frac{1}{2} \left[\left(\frac{10}{2}\right)^{th} observation + \left(\frac{10}{2} + 1 \right)^{th} observation \right]$$
$$\displaystyle = \frac{1}{2} \left[5^{th} observation + 6^{th} observation \right]$$
Median $$\displaystyle = \frac{1}{2} \left[9200 + 10320 \right] = \frac{19520}{2}$$
$$\implies $$ Median $$= 9760$$
$$\therefore$$ Median salary $$= Rs. 9760$$

Question 10

1 / -0

Frequency distribution of distance travelled in kms. per liter of petrol by different mopeds is given below.

Distance travelled (in km/lit)	62 - 65	65 - 68	68 - 71	71 - 74	74 - 77	77 - 80	80 - 83
No.of mopeds	5	8	12	28	35	10	2

Find mean distance travelled per liter of petrol by a moped.

$$71.04$$ kms/lit

$$73.04$$ kms/lit

$$75.04$$ kms/lit

$$79.04$$ kms/lit

Solution

Consider the following table, to calculate mean:

$$ci$$	$$f_i$$	$$x_i$$	$$f_ix_i$$
$$62-65$$	$$5$$	$$63.5$$	$$317.5$$
$$65-68$$	$$8$$	$$66.5$$	$$532$$
$$68-71$$	$$12$$	$$69.5$$	$$834$$
$$71-1-74$$	$$28$$	$$72.5$$	$$2030$$
$$74-77$$	$$35$$	$$75.5$$	$$2642.5$$
$$77-80$$	$$10$$	$$78.5$$	$$785$$
$$80-83$$	$$2$$	$$81.5$$	$$163$$

$$N=\Sigma f_i=100$$

$$\Sigma f_ix_i=7304$$

Mean $$\overline x=\dfrac {\Sigma f_ix_i}{N}$$

$$\therefore \overline x=\dfrac{7304}{100}=73.04$$

Mean distance travelled per liter of petrol by a moped is $$73.04$$ kms/lit

Hence, option $$B$$ is correct.

User

Question Analysis

Correct -
Wrong -
Skipped -

My Perfomance

Score
-
out of -
Rank
-
out of -

Re-Attempt Weekly Quiz Competition

Class-intervals	$$6-10$$	$$10-14$$	$$14-18$$	$$18-22$$	$$22-26$$	$$26-30$$
Frequency	$$ 4$$	$$ 6$$	$$9$$	$$ 12$$	$$ 7 $$	$$2$$

$$ci$$	$$f_i$$	$$x_i$$	$$f_ix_i$$
$$6-10$$	$$4$$	$$ 8$$	$$ 32$$
$$ 10-14$$	$$6$$	$$12$$	$$72$$
$$14-18$$	$$9$$	$$16$$	$$ 144$$
$$18-22$$	$$12$$	$$ 20$$	$$240$$
$$ 22-26$$	$$7$$	$$ 24$$	$$168$$
$$26-30$$	$$ 2$$	$$28$$	$$56$$

Measures of Central Tendency Test - 29

Result

Measures of Central Tendency Test - 29

Score

-

Rank

-

SHARING IS CARING

Question 1

$$194$$

$$185$$

$$197$$

$$220$$

Solution

Question 2

$$271$$

$$292$$

$$257$$

$$243$$

Solution

Question 3

$$74.83$$ seconds

$$79.83$$ seconds

$$83.83$$ seconds

$$86.83$$ seconds

Solution

Question 4

True

False

Can't determine

None of these

Solution

Question 5

$$15.8$$

$$16.8$$

$$17.8$$

None of these

Solution

Question 6

$$6.9$$ months

$$6.16$$ months

$$6.66$$ months

None of these

Solution

Question 7

$$7.5$$

$$7$$

$$8$$

Any number between $$7$$ and $$8$$

Solution

Question 8

$$29.5$$

$$29$$

$$20$$

$$30$$

Solution

Question 9

Rs. $$9670$$

Rs. $$9760$$

Rs. $$6970$$

Rs. $$7960$$

Solution

Question 10

$$71.04$$ kms/lit

$$73.04$$ kms/lit

$$75.04$$ kms/lit

$$79.04$$ kms/lit

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.