Class 10th,- Statistics
Exercise: 14.2 (Solution), Q1 to Q6
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Q1. The following table shows the ages of the patients admitted in 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.
Solution: To find out the modal class, let us the consider the class interval with high frequency
First find the midpoint using the formula,
xi =(upper limit +lower limit)/2
Class Interval | Frequency (fi) | Mid-point (xi) | fixi |
5-15 | 6 | 10 | 60 |
15-25 | 11 | 20 | 220 |
25-35 | 21 | 30 | 630 |
35-45 | 23 | 40 | 920 |
45-55 | 14 | 50 | 700 |
55-65 | 5 | 60 | 300 |
Sum fi = 80 | Sum fixi = 2830 |
The mean formula is
Mean = x̄ = ∑fixi /∑fi
= 2830/80
= 35.37 years
Mean = x̄ = ∑fixi /∑fi
= 2830/80
= 35.37 years
Therefore, the mean of the given data = 35.37 years
Q2. 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.
Q3. 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:
Q3. 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 | 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 |
Calculation for mean: First find the midpoint using the formula,
xi =(upper limit +lower limit)/2
Let us assume a mean, A be 2750
Class Interval | fi | xi | di = xi – a | ui = di/h | fiui |
1000-1500 | 24 | 1250 | -1500 | -3 | -72 |
1500-2000 | 40 | 1750 | -1000 | -2 | -80 |
2000-2500 | 33 | 2250 | -500 | -1 | -33 |
2500-3000 | 28 | 2750 | 0 | 0 | 0 |
3000-3500 | 30 | 3250 | 500 | 1 | 30 |
3500-4000 | 22 | 3750 | 1000 | 2 | 44 |
4000-4500 | 16 | 4250 | 1500 | 3 | 48 |
4500-5000 | 7 | 4750 | 2000 | 4 | 28 |
fi = 200 | fiui = -35 |
The formula to calculate the mean,
Mean = x̄ = a + (∑fiui /∑fi) х h
Mean = x̄ = a + (∑fiui /∑fi) х h
Substitute the values in the given formula
= 2750 + (-35/200) х 500
= 2750 – 87.50
= 2662.50 So, the mean monthly expenditure of the families
= Rupees 2662.50
Q4. 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
= 2750 + (-35/200) х 500
= 2750 – 87.50
= 2662.50 So, the mean monthly expenditure of the families
= Rupees 2662.50
Q4. 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 | 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 |
Calculation of mean:
Find the midpoint using the formula, xi =(upper limit +lower limit)/2
Class Interval | Frequency (fi) | Mid-point (xi) | fixi |
15-20 | 3 | 17.5 | 52.5 |
20-25 | 8 | 22.5 | 180.0 |
25-30 | 9 | 27.5 | 247.5 |
30-35 | 10 | 32.5 | 325.0 |
35-40 | 3 | 37.5 | 112.5 |
40-45 | 0 | 42.5 | 0 |
45-50 | 0 | 47.5 | 0 |
50-55 | 2 | 52.5 | 105.5 |
Sum fi = 35 | Sum fixi = 1022.5 |
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Mean = x̄ = ∑fixi/∑fi
= 1022.5/35
= 29.2
Therefore, mean = 29.2
Q5. The given distribution shows the number of runs scored by some top batsmen of the world in one- day international cricket matches.
Mean = x̄ = ∑fixi/∑fi
= 1022.5/35
= 29.2
Therefore, mean = 29.2
Q5. 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.
Q6. 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:
Q6. 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 |
See next blog for more solution......... Thank you.
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