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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

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

Here, the maximum class frequency is 30 and the class corresponding to frequency is 3000-3500.
So, the modal class = 1500-2000.
Thus, we haveModal class = 1500-2000
l = 1500
f₁ = 40, f₀ = 24, f₂ = 33 and h = 500
Now, substituting these values in the formula of mode, we get

$Mode space equals space straight l plus open square brackets fraction numerator straight f subscript straight i minus straight f subscript 0 over denominator 2 straight f subscript straight i minus straight f subscript 0 minus straight f subscript 2 end fraction close square brackets straight x space straight h space equals space 1500 plus open square brackets fraction numerator 40 minus 24 over denominator 2 cross times 40 minus 24 minus 33 end fraction close square brackets space straight x space 500 space space space space space space space space equals space 1500 plus open parentheses fraction numerator 16 over denominator 80 minus 57 end fraction close parentheses cross times 500 equals 1500 plus fraction numerator 16 cross times 500 over denominator 23 end fraction equals 1500 plus 8000 over 23 equals 1500 plus 347.83 equals 1847.83$

Hence, the modal monthly expenditure of the families is Rs. 1847.83.
Finding Mean:

Expenditure (in Rs.)

Number of families

1000-1500

24

1500-20

Here, we have $sum from blank to blank of f subscript i equals 200 comma space sum from blank to blank of f subscript i u subscript i equals space minus 235 comma space h space equals space 500 space a n d space A space equals space 3250$

Now, $top enclose straight x space equals space A space plus space open parentheses fraction numerator begin display style sum from blank to blank of end style f subscript i u subscript 1 over denominator begin display style sum from blank to blank of end style f subscript i end fraction close parentheses space x space h space equals space 3250 space plus space open parentheses fraction numerator negative 235 over denominator 200 end fraction close parentheses space x space 500 space equals space 3250 space minus fraction numerator 235 space x space 5 over denominator 2 end fraction equals 3250 minus 1175 over 2$

= 3250 - 587.50 = 2662.50
Hence, the mean monthly expenditure is Rs. 2662.50.

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

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