The following data gives the information on the observed lifetimes (in hours) of 225 electrical comp

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Question 2 The following data gives the information on the observed lifetimes (in hours) of 225 electrical components:

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

Determine the modal lifetimes of the components.

Solution:

From the given data the modal class is 60–80.

Lower limit of modal class = l = 60,

The frequencies are:

$f_m$ = 61,$ f_{1}$ = 52, $f_{2}$ = 38 and h = 20

The formula to find the mode is

Mode =$ l+ [\dfrac{(f_m – f_{1})}{(2f_m – f_{1} – f_{2})}] × h$

Substitute the values in the formula, we get

Mode = 60 + $[\dfrac{(61 – 52)}{(122 – 52 – 38)}]$ × 20

Mode = 60 + $[\dfrac{(9 × 20)}{32}]$

Mode = 60 + $(\dfrac{45}{8})$ = 60 + 5.625

Therefore, modal lifetime of the components = 65.625 hours.

Additional Questions

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

Answer

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

No of students per teacher	$\dfrac{Number of states} {U.T}$
15-20	3
20-25	8
25- 30	9
30-35	10
35-40	3
40-45	0
45- 50	0
50-55	2

Answer

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

Run 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.

Answer

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

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

Answer

The following table shows the ages of the patients admitted to a hospital during a year:

Age (in years)	5-15	15-25	25-35	35- 45	45-55	55-65
Number of patients	6	11	21	23	14	5

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

Answer

The following data gives the information on the observed lifetimes (in hours) of 225 electrical components:

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

Determine the modal lifetimes of the components.

Answer

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

Answer

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

No of students per teacher	$\dfrac{Number of states} {U.T}$
15-20	3
20-25	8
25- 30	9
30-35	10
35-40	3
40-45	0
45- 50	0
50-55	2

Answer

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

Run 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.

Answer

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

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

Answer

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