Statistics Test

Result

Statistics Test - 37

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

If mode = $$80$$ and mean = $$110$$, then the median is

A
$$110$$

B
$$120$$

C
$$100$$

D
$$90$$

Solution

Given, mode $$= 80$$, mean $$= 110$$
We know, Mode $$= 3$$ (median) $$- 2$$ (mean)
$$80 = 3$$ (median) $$- 2 (110)$$
$$3$$ (Median) $$= 80 + 220$$
Median $$ \displaystyle =\frac{300}{3}=100$$
Question 2
1 / -0

Find the value of $$p$$ if the mean of the following distribution is $$20$$.
$$x$$ 15 17 19 20 + $$p$$ 23
$$f$$ 2 3 4 5$$p$$ 6

A
$$p = 0$$

B
$$p = 1$$

C
$$p = 2$$

D
Data insufficient

Solution

$$x$$ $$f$$ $$fx$$
$$15$$ $$2$$ $$30$$
$$17$$ $$3$$ $$51$$
$$19$$ $$4$$ $$76$$
$$(20+p)$$
$$5p$$ $$\displaystyle 100p+5p^{2}$$
$$23$$ $$6$$ $$138$$

$$\displaystyle \sum f=15+5p$$

$$\displaystyle \sum fx=295+100p+5p^{2}$$

Mean $$\overline{x}=\dfrac{\sum fx}{\sum f}=\dfrac{295+100p+5p^{2}}{15+5p}$$

$$\displaystyle \Rightarrow 20=\frac{295+100p+5p^{2}}{15+5p}$$

$$\displaystyle \Rightarrow 300+100p=295+100p+5p^{2}$$

$$\displaystyle \Rightarrow 5p^{2}=5$$

$$\Rightarrow p=1$$ or $$-1$$

Question 3

1 / -0

The mean of the following distribution is

Class	$$0-5$$	$$5-10$$	$$10-15$$	$$15-20$$	$$20-25$$	$$25-30$$
Frequency	$$4$$	$$5$$	$$7$$	$$12$$	$$7$$	$$5$$

$$15$$

$$16$$

$$17$$

$$18$$

Solution

Answer:-

$$x_i=\cfrac{\text{upper limt + lower limit}}{2}$$

Class	Frequency	$$x_i$$	$$x_i.f_i$$
$$0-5$$	$$4$$	$$2.5$$	$$6$$
$$5-10$$	$$5$$	$$7.5$$	$$37.5$$
$$10-15$$	$$7$$	$$12.5$$	$$87.5$$
$$15-20$$	$$12$$	$$17.5$$	$$210$$
$$20-25$$	$$7$$	$$22.5$$	$$157.5$$
$$25-30$$	$$5$$	$$27.5 $$	$$137.5$$
	$$\Sigma f_i=40$$		$$\Sigma f_i.x_i=640$$

Mean =$$ \cfrac { \Sigma f_{ i }.x_{ i } }{ \Sigma f_{ i } } =\cfrac { 640 }{ 40 } =16$$

Question 4
1 / -0

Calculate the median from the following data
Rent (in Rs.) 15-25 25-35 35-45 45-55 55-65 65-75 75-85 85-95
No. of Houses 8 10 15 25 40 20 15 7

A
$$58$$

B
$$61$$

C
$$59$$

D
$$63$$

Solution

Rent No. of houses C. F.
15-25 8 8
25-35 10 18
35-45 15 33
45-55 25 58
55-65 40 98
65-75 20 118
75-85 15 133
85-95 7 140
$$\Sigma f_i = 140$$
$$\cfrac{N}{2}=\cfrac{140}{2}=70$$
$$\Rightarrow\; \text{98 is just greater than 70} \therefore\; \text{Median class is 55-65.}$$
Median $$=L+\cfrac{\cfrac{N}{2}-C}{f}\times w$$
L = Lower limit of median class $$= 55$$
C = C.F. of class preceding the median class $$= 58$$
f = frequency of median class $$= 40$$
w = width of median class $$= 65-55 = 10$$
Median $$=55+\cfrac{70-58}{40}\times 10\;=\;55+\cfrac{12}{4}\;=\;58$$
A) 58
Question 5
1 / -0

Find the mode of the following distribution
Daily Wages 31-36 37-42 43-48 49-54 55-60 61-66
No. of workers 6 12 20 15 9 4

A
$$48.5$$

B
$$47.5$$

C
$$46.2$$

D
$$48.3$$

Solution

Converting the given class interval into continuous class interval; Adding $$0.5$$ to upper limit and subtracting $$0.5$$ to lower limit.
Daily wages No. of workers
30.5-36.5 6
36.5-42.5 12
42.5-48.5 20
48.5-54.5 15
54.5-60.5 9
60.5-66.5 4
Since the maximum frequency is of class $$42.5-48.5$$ i.e. $$20.$$ Hence the modal class is $$42.5-48.5$$.
Mode = $$l+\cfrac{f_1-f_0}{2f_1-f_0-f_2}\times h$$
$$l =$$ lower limit of modal class $$= 42.5$$
$$f_1$$ = frequency of modal class $$= 20$$
$$f_0$$ = frequency of class before modal class $$= 12$$
$$f_2$$ = frequency of class after modal class $$= 15$$
h = width of modal class$$= 48.5-42.5 = 6$$
$$\therefore \; Mode=42.5+\cfrac{20-12}{\left(2\times 20\right)-12-15}\times 6 = 46.5 \simeq 46.2$$
Question 6
1 / -0

Calculate the median for the following distribution class
Class 0-10 10-20 20-30 30-40 40-50 50-60
Frequency 5 10 20 7 8 5

A
$$26.25$$

B
$$22$$

C
$$29$$

D
None of these

Solution

Total frequency $$=$$ $$55$$.
So, $$\dfrac{55}{2}=27.5$$ which lies in class $$20-30$$.
Hence, median is in group $$20-30$$
Estimated median $$= L+\dfrac{n/2-B}{G}W$$,
where $$L$$ $$=$$ Lower class boundary of the group containing the median
$$n$$ $$=$$ Total frequency
$$B$$ $$=$$ total frequency before the median group
$$G$$ $$=$$ frequency of the median
$$W$$ $$=$$ class width
$$=20+\dfrac{(55/2)-15}{20}.10$$
$$=26.25$$
Question 7
1 / -0

Which of the following is correct for the given data $$55, 38, 69, 24, 89$$?

A
$$median=mode$$

B
$$mean=mode$$

C
$$mean=median$$

D
None of these

Solution

$$24, 38, 55, 69, 89$$

$$Mean = \dfrac{sum\ of \ all \ the\ terms}{total\ number\ of\ terms} $$

$$Mean = \dfrac{24+38+55+69+89}{5}$$

$$Mean=\dfrac {275}{5}=55$$
if n (total number of terms ) is odd then the middle term when the data is arranged in ascending order is median
Arranging the data in ascending order, we get :
$$24, 38, 55, 69, 89$$
$$Median=55$$
Therefore, for the given data,$$Mean=median$$

Question 8

1 / -0

Calculate the median in the following frequency distribution

Wages	50-60	60-70	70-80	80-90	90-100
No. of labourers	5	10	15	20	25

$$90$$

$$70$$

$$83.75$$

$$85$$

Solution

Wages	mid point (m)	frequency (f)	(m-75)/10 (d)	fd	c.f.
50-60	55	5	-2	-10	5
60-70	65	10	-1	-10	15
70-80	75	15	0	0	30
80-90	85	20	1	20	50
90-100	95	25	2	50	75
		n=75		$$\sum fd=50$$

Median is given by $$L+\dfrac{\dfrac n2 -c.f.}{f}\times i$$

where $$L$$ is the lower limit of the median class. (median class is the class where $$\dfrac n2^{th}$$ term is lying)

$$c.f.$$ is the cumulative frequency of the class preceding the median class

$$f$$ is the frequency of the median class

$$i$$ is the class interval of the median class.

From the above table,

$$L=70$$

$$\dfrac n2 =37.5$$

$$c.f.=15$$

$$f=15$$

$$i=10$$

Therefore, $$median=70+\dfrac{37.5 -15}{15}\times 10=70+15=85$$

Question 9
1 / -0

Calculate the median from the following distribution
Class 5-10 10-15 15-20
5 6 15
Class 20-25 25-30 30-35
10 5 4
Class 35-40 40-45
2 2

A
$$20.5$$

B
$$18.5$$

C
$$19.5$$

D
$$21$$

Solution

Prepare the cumulative table. $$N = 49$$
$$\Rightarrow \frac {N}{2}=24.5$$
cumulative frequency $$> \frac {N}{2}$$ corresponds to 15-20 (median class)
$$Median=l+\frac {\frac {N}{2}-F_1}{F}\times h=$$
$$15+\frac {24.5-11}{15}\times 5=19.5$$.

Question 10

1 / -0

Find the mean

Age (yrs)	7	8	9	10	11
No. of Students	5	6	4	12	7

9.3

8.7

11.9

5.2 Solution

$$Age(yrs)$$ $$x_i$$	$$No.of\,students$$ $$f_i$$	$$f_ix_i$$
$$7$$	$$5$$	$$35$$
$$8$$	$$6$$	$$48$$
$$9$$	$$4$$	$$36$$
$$10$$	$$12$$	$$120$$
$$11$$	$$7$$	$$77$$
	$$\sum f_i=34$$	$$\sum f_ix_i=316$$

$$\Rightarrow$$ $$Mean=\dfrac{\sum f_ix_i}{f_i}=\dfrac{316}{34}=9.3$$

User

Question Analysis

Correct -
Wrong -
Skipped -

My Perfomance

Score
-
out of -
Rank
-
out of -

Re-Attempt Weekly Quiz Competition

$$x$$	$$f$$	$$fx$$
$$15$$	$$2$$	$$30$$
$$17$$	$$3$$	$$51$$
$$19$$	$$4$$	$$76$$
$$(20+p)$$	$$5p$$	$$\displaystyle 100p+5p^{2}$$
$$23$$	$$6$$	$$138$$

Rent (in Rs.)	15-25	25-35	35-45	45-55	55-65	65-75	75-85	85-95
No. of Houses	8	10	15	25	40	20	15	7

Rent	No. of houses	C. F.
15-25	8	8
25-35	10	18
35-45	15	33
45-55	25	58
55-65	40	98
65-75	20	118
75-85	15	133
85-95	7	140
	$$\Sigma f_i = 140$$

Daily Wages	31-36	37-42	43-48	49-54	55-60	61-66
No. of workers	6	12	20	15	9	4

Daily wages	No. of workers
30.5-36.5	6
36.5-42.5	12
42.5-48.5	20
48.5-54.5	15
54.5-60.5	9
60.5-66.5	4

Class	5-10	10-15	15-20
	5	6	15
Class	20-25	25-30	30-35
	10	5	4
Class	35-40	40-45
	2	2

$$x$$	15	17	19	20 + $$p$$	23
$$f$$	2	3	4	5$$p$$	6

Class	0-10	10-20	20-30	30-40	40-50	50-60
Frequency	5	10	20	7	8	5

Statistics Test - 37

Result

Statistics Test - 37

Score

-

Rank

-

SHARING IS CARING

Question 1

$$110$$

$$120$$

$$100$$

$$90$$

Solution

Question 2

$$p = 0$$

$$p = 1$$

$$p = 2$$

Data insufficient

Solution

Question 3

$$15$$

$$16$$

$$17$$

$$18$$

Solution

Question 4

$$58$$

$$61$$

$$59$$

$$63$$

Solution

Question 5

$$48.5$$

$$47.5$$

$$46.2$$

$$48.3$$

Solution

Question 6

$$26.25$$

$$22$$

$$29$$

None of these

Solution

Question 7

$$median=mode$$

$$mean=mode$$

$$mean=median$$

None of these

Solution

Question 8

$$90$$

$$70$$

$$83.75$$

$$85$$

Solution

Question 9

$$20.5$$

$$18.5$$

$$19.5$$

$$21$$

Solution

Question 10

9.3

8.7

11.9

5.2

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.