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Marks obtained by 200 students in an examination are given below:

Marks |
No.of students |

0-10 | 5 |

10-20 | 11 |

20-30 | 10 |

30-40 | 20 |

40-50 | 28 |

50-60 | 37 |

60-70 | 40 |

70-80 | 29 |

80-90 | 14 |

90-100 | 6 |

Draw an ogive for the given distribution taking 2 cm = 10 marks on one axis and 2 cm = 20 students on the other axis. Using the graph, determine

1) The median marks.

2) The number of students who failed if minimum marks required to pass is 40.

3) If scoring 85 and more marks are considered as grade one, find the number of students who secured grade one in the examination.

Income of 100 students of their parents is given as follows

Income (in thousand Rs.) |
No. of students (f) |

0 - 8 | 8 |

8 - 16 | 35 |

16 - 24 | 35 |

24 - 32 | 14 |

32 - 40 | 8 |

Draw an ogive for the given distribution on a graph sheet.

Use a suitable scale for your ogive. Use your ogive to estimate:

(i) the median income.

(ii) Calculate the income below which freeship will be awarded to students if their parents income is in the bottom 15%

(iii) Mean income.

Class mark |
12.5 | 17.5 | 22.5 | 27.5 | 32.5 | 32.5 | 42.5 |

Frequency |
12 | 17 | 22 | 27 | 30 | 21 | 16 |

(a) From the distribution, given above, construct a frequency table.

(b) Use the table obtained in part (a) to draw: (i) a histogram, (ii) an ogive

The marks obtained by 120 students in a test are given below:

Marks | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 | 80-90 | 90-100 |

No. of students |
5 | 9 | 16 | 22 | 26 | 18 | 11 | 6 | 4 | 3 |

Draw an ogive for the given distribution on a graph sheet.

Use a suitable scale for ogive to estimate the following:

(1) The median.

(2) The number of students who obtained more than 75% marks in the test.

(3) The number of students who did not pass the test if minimum marks required to pass is 40

The table shows the distribution of the scores obtained by 160 shooters in a shooting competition. Use a graph sheet and draw an ogive for the distribution. (Take 2 cm = 10 scores on the X-axis and 2 cm = 20 shooters on the Y-axis).

Scores | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 | 80-90 | 90-100 |

No. of shooters |
9 | 13 | 20 | 26 | 30 | 22 | 15 | 10 | 8 | 7 |

Use your graph to estimate the following:

1) The median

2) The interquartile range.

3) The number of shooters who obtained a score of more than 85%.

The following table shows the distribution of the heights of a group of factory workers:

Ht. (cm) |
150 - 155 |
155 – 160 |
160 - 165 |
165 – 170 |
170 – 175 |
175 - 180 |
180 – 185 |

No of workers: |
6 | 12 | 18 | 20 | 13 | 8 | 6 |

(i) Determine the cumulative frequencies.

(ii) Draw the ‘less than’ cumulative frequency curve on graph paper. Use 2 cm = 5 cm height on one axis and 2 cm = 10 workers on the other.

Use graph paper for this question.

The table given below shows the monthly wages of some factory workers

(i) Using the table, calculate the cumulative frequencies of workers

(ii) Draw a cumulative frequency curve.

Use 2 cm = ₹ 500, starting the origin at ₹ 6500 on x-axis, and 2 cm = 10 workers on the y – axis.

Wages (in Rs) | 6500-7000 | 7000-7500 | 7500-8000 | 8000-8500 | 8500-9000 | 9000-9500 | 9500-10000 |

No of workers | 10 | 18 | 22 | 25 | 17 | 10 | 8 |