Statistic Long Questions (Question 2)


Question 2:
The data below shows the mass, in kg, of 50 students.

60       50       52       44      49      67      61      43       62      53  

47       54       58       60      56      41      69      45       51      63

56       58       59       47      48      45      65      47       58      51

64       62       60       56      56      61      64      57       62      64

64       46       48       61      60      63      53      43       63      62


(a) Copy and complete the table below based on the data above.  
Mass (kg)
Midpoint
Frequency
40 – 44
42
45 – 49
(b) Based on the completed table above,
 (i) State the size of the class interval used in the table.
 (ii) Calculate the estimated mean of the mass of the students.

For this part of the question, use graph paper.
(c) By using a scale of 2cm to 5 kg on the horizontal axis and 2cm to 2 students on the vertical axis, draw a frequency polygon for the data.


Solution:
(a)
Mass (kg)
Midpoint
Frequency
40 – 44
42
4
45 – 49
47
9
50 – 54
52
7
55 – 59
57
9
60 – 64
62
18
65 – 69
67
3

(b)(i)
Size of class interval
= upper boundary – lower boundary
= 44.5 – 39.5
= 5

(b)(ii)
Estimated mean = 42 × 4 + 47 × 9 + 52 × 7 + 57 × 9 + 62 × 18 + 67 × 3 50 = 2785 50 = 55.7
(c) 

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