CBSE 10 Mathematics Statistics Practice Paper 12
1. The marks obtained by 30 students of Class X of a certain school in a Mathematics paper consisting of 100 marks are presented in table below. Find the mean of the marks obtained by the students.
| Marks Obtained (\(x_i\)) | | 10 | 20 | 36 | 40 | 50 | 56 | 60 | 70 | 72 | 80 | 88 | 92 | 95 |
| Number of students \((f_i)\) | | 1 | 1 | 3 | 4 | 3 | 2 | 4 | 4 | 1 | 1 | 2 | 3 | 1 |
2. The table below gives the percentage distribution of female teachers in the primary schools of rural areas of various states and union territories (U.T.) of India. Find the mean percentage of female teachers by all the three methods discussed in this section.
| Percentage of female teachers | | 15 - 25 | 25 - 35 | 35 - 45 | 45 - 55 | 55 - 65 | 65 - 75 | 75 - 85 |
| Number of States/U.T. | | 6 | 11 | 7 | 4 | 4 | 2 | 1 |
3. The following distribution shows the daily pocket allowance of children of a locality. The mean pocket allowance is Rs 18. Find the missing frequency f.
| Daily pocketallowance (in Rs) | | 11 - 13 | 13 - 15 | 15 - 17 | 17 - 19 | 19 - 21 | 21 - 23 | 23 - 25 |
| Number of children | | 7 | 6 | 9 | 13 | f | 5 | 4 |
4. A survey conducted on 20 households in a locality by a group of students resulted in the following frequency table for the number of family members in a household. Find the mode of this data.
| Family size | | 1 - 3 | 3 - 5 | 5 - 7 | 7 - 9 | 9 - 11 |
| Number of families | | 7 | 8 | 2 | 2 | 1 |
5. 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
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Find the mode and the mean of the data given above. Compare and interpret the two measures of central tendency.
6. 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 :
| Number of 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 |
7. 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 (in units) | | Number of consumers |
| 65 - 85 | | 4 |
| 85 - 105 | | 5 |
| 105 - 125 | | 13 |
| 125 - 145 | | 20 |
| 145 - 165 | | 14 |
| 165 - 185 | | 8 |
| 185 - 205 | | 4 |
8. 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 | | 60 |
9. 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 mm) | | 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.
10. The following table gives the distribution of the life time of 400 neon lamps :
| Life time (in hours) | | life time of a lamp |
| 1500 - 2000 | | 14 |
| 2000 - 2500 | | 56 |
| 2500 - 3000 | | 60 |
| 3000 - 3500 | | 86 |
| 3500 - 4000 | | 74 |
| 4000 - 4500 | | 62 |
| 4500 - 5000 | | 48 |
Find the median life time of a lamp.
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