This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Mathematics Form 4 Chapter 6 : Statistics III
CHAPTER 6 : STATISTICS III
(a) Mode of a ungrounded data
Mode = the value of data with the highest frequency
Example 1 :
6, 7, 7, 11, 5, 6, 11, 13, 14, 11, 8
5, 6, 6, 7, 7, 8, 11, 11, 11, 13, 14
mode = 11
Example 2 :
Score 2 4 6 8 10
Frequency 3 15 7 12 9
mode = 4
Example 3 :
Score 0 1 2 3 4
Frequency 1 3 7 x 5
If mode = 2, the maximum value of x = ???
x < 7 x = 6
Example 4 :
Score 0 1 2 3 4
Frequency 1 7 0 x 2
If mode = 3, the minimum value of x = ???
x > 7 x = 8
(b) Median of a ungrounded data
Median = the middle value when a set of data is arranged in ascending order
(d) For this part of the question, use the graph paper provided on the next page.
By using a scale of 2 cm to 5 years on the x-axis and 2 cm to one worker on the y-axis, draw a histogram for the data.
[4 marks]
Answer :
(d) Refer graph on the next page.
2 The data shows the masses, in kg, of suitcases carried by a group of tourists. Each tourist has one suitcase.
27 10 22 28 21 14 29 25
29 18 22 13 20 21 24 27
27 25 16 19 16 24 26 27
29 19 33 25 23 24 26 31
(a) Based on the data above, and by using the a class interval of 3 kg, complete the table in the answer space. [3 marks]
(b) Based on the table in (a), calculate the estimated mean mass of the suitcases and give your answer correct to 2 decimal places. (Ans : 23.19) [3 marks]
(c) For this part of the question, use the graph paper provided on the next page.
By using a scale of 2 cm to 3 kg on the horizontal axis and 2 cm to one suitcase on the vertical axis, draw a histogram for the data. [4 marks]
(d) State one information that can be obtained from the histogram in (c). [2 marks]
3 The data shows the masses, in kg, for a group of 32 students.
44 64 59 49 35 40 50 51 51 59 51
60 50 40 43 47 45 57 53 52 56 56
54 49 58 54 48 47 53 45 62 46
(a) In the answer space, construct a frequency table for the above data by using 5 kg as the size of the class interval. Begin with 30 – 34, 35 – 39, and so on.
[3 marks]
(b) Based on the table in (a),
(i) state the modal class, (Ans : 50 – 54)
(ii) estimate the mean mass. (Ans : 50.906)[4
marks]
(c) For this part of the question, use the graph paper provided on the next page.
By using a scale of 2 cm to 5 kg on the x-axis and 2 cm to one student on the y-axis, draw a histogram for the data.
[4 marks]
(d) On the histogram, draw a frequency polygon for the data.[1 mark]
9 The table show the distribution of marks obtained by a group of 80 students in a Mathematics test.
Marks Frequency Cumulative Frequency
51 - 55 4 4
56 - 60 9 13
61 - 65 17 30
66 - 70 x 50
71 - 75 15 65
76 - 80 8 y
81 - 85 5 78
86 - 90 2 80
(a) Based on the table, find
(i) the value of x, (Ans : 20)
(ii) the value of y, (Ans : 73)
(iii) the mid-point of the modal class. (Ans : 68) [4 marks]
(b) For this part of the question, use the graph paper provided on the next page.By using a scale of 2 cm to 5 marks on the horizontal axis and 2 cm to 10 students on the vertical axis, draw an ogive for the data. [4 marks]
(c) From the ogive, find
(i) the lower quartile, (Ans : 62.5)
(ii) the median, (Ans : 67.5)
(iii) the passing mark, if only 3 students failed in the test. (Ans : 54.5)
(iv) the minimum mark to score an A, if only 5 students scored A in the test. (Ans : 82)[4 marks]
10 The table shows the distribution of heights, in m, of 92 trees in a Recreation Park.
Height (m) Frequency
1.0 - 1.4 2
1.5 - 1.9 9
2.0 - 2.4 26
2.5 - 2.9 24
3.0 - 3.4 19
3.3 - 3.9 8
4.0 - 4.4 3
4.5 - 4.9 1
(a) Calculate the range for the grouped data above. (Ans : 3.5) [2 marks]Answer :
(a)
(b) Based on the table above, complete the cumulative frequency table in the answer space.[3 marks]
Answer :Class Interval Upper Boundary Cumulative
Frequency
1.0 - 1.4
1.5 - 1.9
2.0 - 2.4
2.5 - 2.9
3.0 - 3.4
3.5 - 3.9
4.0 - 4.4
4.5 - 4.9
(c) For this part of the question, use the graph paper provided on the next page.By using a scale of 2 cm to 0.5 m on the x-axis and 2 cm to 10 trees on the y-axis, draw an ogive for the data. [4 marks]
Answer :
(c) Refer graph on the next page.
(d) From the ogive, find
(i) the median, (Ans : 2.65)
(ii) the interquartile range, (Ans : 1)
(iii) find the percentage of trees which are at least 4.1 m in height and give your answer correct to 2 decimal places. (Ans : 3.26) [3 marks]