#### Question

The final marks in mathematics of 30 students are as follows:

53, 61, 48, 60, 78, 68, 55, 100,67,90

75,88,77,37,84,58,60,48,62,56

44, 58, 52, 64, 98, 59, 70, 39, 50, 60

(i) Arrange these marks in the ascending order, 30 to 39 one group, 40 to 49 second group etc.

Now answer the following:

(ii) What is the highest score?

(iii) What is the lowest score?

(iv) What is the range?

(v) If 40 is the pass mark how many have failed?

(vi) How many have scored 75 or more?

(vii) Which observations between 50 and 60 have not actually appeared?

(viii) How many have scored less than 50?

#### Solution

The final marks in mathematics of 30 students are as follows:

53, 61, 48, 60, 78, 68, 55, 100, 67, 90, 75, 88, 77, 37, 84, 58, 60, 48, 62, 56, 44, 58, 52, 64,

98, 59, 70, 39, 50, 60.

(i) | Group | Observations |

I(30–39) | 37, 39 | |

II(40–49) | 44, 48, 48 | |

III(50–59) | 50, 52, 53, 55, 56, 58, 58, 59 | |

IV(60–69) | 60, 60, 60, 61, 62, 64, 67, 68 | |

V(70–79) | 70, 55, 77, 78 | |

VI(80–89) | 84, 88 | |

VII(90–99) | 90, 98 | |

VIII(100–109) | 100 |

(ii) Highest score = 100

(iii) Lowest score = 37

(iv) Range = 100 – 37 = 63

(v) If 40 is the pass mark, 2 students have failed

(vi) 8 students have scored 75 or more

(vii) Observation 51, 54, 57 between 50 and 60 have not actually appeared

(viii) 5 students have scored less than 50