The final mark in mathematic of 30 student are as follow:

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 |

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 given raw data can be arranged in an ascending order. The class intervals are 30\[-\]39, 40 \[-\]49,...100 \[-\] 09. Then, take the raw data and place it in the appropriate class intervals.

(i) The marks can be arranged in an ascending order as shown below:

30 to 39\[\to\]37, 39

40 to 49\[\to\]44, 48, 48

50 to 59\[\to\] 50, 52, 53,

55, 56, 58, 58, 59

60 to 69\[\to\] 60, 60, 60, 61, 62, 64, 67, 68

70 to 79\[\to\]70, 75, 77, 78

80 to 89\[\to\] 84, 88

90 to 99\[\to\]90, 98

100 to 109\[\to\]100

(ii) The highest score is 100.

(iii) The lowest score is 37.

(iv) The range is 100 \[-\] 37, i.e. 63.

(v) If 40 is the passing mark, then the number of students who failed is 2 (i.e. 37, 39).

(vi) The number of students scoring 75 and above is 8 (i.e. 75, 77, 78, 84, 88, 90, 98, 100).

(vii) The marks 51, 54, and 57 do not actually appear between 50 and 60.

(viii) The number of students scoring less than 50 is 5 (i.e. 37, 39, 44, 48, 48).