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Statistics

Long Answer Type

231.

The following table shows the ages of the patients admitted in a hospital during a year.

Find the mode and mean of the data given below. Compare and interpret the measures of central tendency.

Age (in yrs)	No. of patients
5-15	6
15-25	11
25-35	21
35-45	23
45-55	14
55-65	5

282 Views

Short Answer Type

232.

The following data gives the information on the observed life-times (in hours) of 225 electrical components.

Life time (in hours)	Frequency
0-20	10
20-40	35
40-60	52
60-80	61
80-100	38
100-120	29

Determine the modal lifetimes of the components.

264 Views

Long Answer Type

233.

The following data gives the distribution of total monthly household expenditure of 200 families of a village. Find the modal monthly expenditure of the families. Also, find the mean monthly expenditure:

Expenditure (in Rs.)	Number of families
1000-1500	24
1500-2000	40
2000-2500	33
2500-3000	28
3000-3500	30
3500-4000	22
4000-4500	16
4500-5000	7

234 Views

Short Answer Type

234.

The following distribution gives the state-wise teacher-student ratio in higher secondary schools of India. Find the mode and mean of this data. Interpret the two measures.

Number of students per teacher	Number of states/U.T.
15-20	3
20-25	8
25-30	9
30-35	10
35-40	3
40-45	0
45-50	0
50-55	2

309 Views

235.

The given distribution shows the number of runs scored by some top batsmen of the world in one-day international cricket matches.

Runs scored	Number of batsman
3000-4000	4
4000-5000	18
5000-6000	9
6000-7000	7
7000-8000	6
8000-9000	3
9000-10000	1
10000-11000	1

Find the mode of the data.

215 Views

236.

A student noted the number of cars passing through a spot on a road for 100 periods each of 3 minutes and summarised it in the table given below. Find the mode of the data :

Numberof cars	0-10	10-20	20-30	30-40	40-50	50-60	60-70	70-80
Frequency	7	14	13	12	20	11	15	8

109 Views

237.
The following frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Find the median, mean and mode of the data and compare them.

Monthly consumption of electricity (in units)

Number of consumers

68-85

4

85-105

5

105-125

13

125-145

20

145-165

14

165-185

8

185-205

4

Finding Median:

Monthly consumption of electricity (in units)	Number of consumers	Cumulative frequency
68-85	4	4
85-105	5	9
105-125	13	22
125-145	20	42
145-165	14	56
165-185	8	64
185-205	4	68
	n = 68

We have n = 68. So,

open parentheses straight n over 2 close parentheses

th observation = 34th observation.
So, median lies in the group of 125-145 i.e. median class = 125-145

Now, we have median class = 125.145, i = 125,

straight n over 2

= 34, cf = 22, f = 20 and h =20
Substituting these values in the formula of median, we get

Median space equals space l italic space plus space open square brackets fraction numerator begin display style straight n over 2 end style minus cf over denominator straight f end fraction close square brackets straight x space straight h space equals space 125 plus open square brackets fraction numerator 34 minus 22 over denominator 20 end fraction close square brackets space straight x space 20 space equals space 125 space plus space 12 space equals space 137 space units.

Finding Mean:

Finding Median:

Monthly consumption of electricity (in units)

Numb

Here. we have

sum from blank to blank of f subscript i space equals space 68 comma space sum from blank to blank of f subscript i u subscript i space end subscript equals 7 comma space h space equals space 20 space a n d space A space equals space 135

Now,

top enclose straight x space equals space A plus fraction numerator begin display style sum from blank to blank of end style f subscript i u subscript i over denominator begin display style sum from blank to blank of end style f subscript i end fraction space x space h

equals space 135 plus 7 over 68 straight x space 20 equals space 135 plus 35 over 17 equals 135 plus 2.05 equals 137.05

Finding Mode :
Here, the maximum class frequency is 20 and the class corresponding to frequency is 125-145.
So, the modal class = 125-145.
Thus, we have, Modal class = 125-145, l = 125, f₁ = 20, f₀ = 13, f₂= 14, and h = 20
Now, substituting these values in the formula of mode, we get

$Mode space equals space l plus open square brackets fraction numerator straight f subscript straight i minus straight f subscript 0 over denominator 2 straight f subscript 1 minus straight f subscript 0 minus straight f subscript 2 end fraction close square brackets space straight x space straight h space equals space 125 plus open square brackets fraction numerator 20 minus 13 over denominator 2 space straight x space 20 minus 13 minus 14 end fraction close square brackets space straight x space 20 space equals space 125 plus open square brackets fraction numerator 7 over denominator 40 minus 17 end fraction close square brackets space straight x space 20 space space space space space space space space equals space 125 plus 140 over 13 equals 125 plus 10.76 equals 135.76 space units.$
Comparison: On comparison, we find that the three measures are approximately the same in this case.

303 Views

238.

If the median of the distribution given below is 28.5, find the values of x and y.

Class interval	Frequency
0-10	5
10-20	x
20-30	20
30-40	15
40-50	y
50-60	5
Total	x = 60

3584 Views

239.

A life insurance agent found the folio wing data for distribution of ages of 100 policy holders. Calculate the median age, if policies are only given to persons having age 18 yrs. onwards but less than 60 years.

Age (in yrs.)	No. of policy holders
below 20	2
below 25	6
below 30	24
below 35	45
below 40	78
below 45	89
below 50	92
below 55	98
below 60	100

213 Views

240.

The lengths of 40 leaves of a plant are measured correct to the nearest millimetre and the data obtained is represented in the following table:

Length (in nun)	Number of leaves
118-126	3
127-135	5
136-144	9
145-153	12
154-162	5
163-171	4
172-180	2

Find the median length of the leaves.

241 Views