[PDF] Sec-4-Statistics-1-Cumulative-Frequency-Tables-and-Curves

69465_3Sec_4_Statistics_1_Cumulative_Frequency_Tables_and_Curves_Assignment.pdf www.jimmymaths.com

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Name: ___________________

(Sec 4) Statistical Data Analysis - Cumulative Frequency Tables and

Curves

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EHORZ (i) How many people participated in the survey? (ii) Using a scale of 1 cm to represent 1 hour on the horizonal axis and 1 cm to represent 10 students on the vertical axis, draw the cumulative frequency curve for the given data. (iii) Use your curve in (ii) to estimate (a) the number of adults who get 6.5 hours or less of sleep on average, (b) the number of adults who sleep for more than 8.5 hours, (c) the value of t, such that 75% of the adults surveyed sleep for at least t hours or less.

No. of Hours, t Cumulative Frequency

3t 0 4t 1 5t 7 6t 22
7t 38
8t 62
9t 75
10t 80
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Length (cm), x Frequency

12x 0

12 14x

10

14 16x

18

16 18x

30

18 20x

30

20 22x

10

22 24x

2 (i) Construct a table of cumulative frequencies for the given data. (ii) Using a scale of 1 cm to represent 2 cm on the horizonal axis and 1 cm to represent 10 mudskippers on the vertical axis, draw the cumulative frequency curve for the given data. (iii) The average length of a mudskipper is normally 17 cm. Use your curve in (ii) to calculate the percentage of this group that is of average size or below. (iv) Calculate an estimate for the mean length of this particular group of mudskippers. (v) Based on your estimate, what can you say about the lengths of this group of 100 mudskippers compared to the normal average of 17 cm? www.jimmymaths.com

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(i) From the graph, estimate (a) the number of PMDs with speeds less than or equal to 10 km/h, (b) the number of PMDs with speeds less than or equal to 15 km/h, (c) the percentage of PMDs with speeds greater than 25 km/h. (ii) A PMD is selected at random from the group. Find the probability that the speed of the randomly selected PMD is (a) greater than 25 km/h, (b) either not greater than 10 km/h or greater than 25 km/h. (iii) If two PMDs are chosen at random from the group, find the probability that the speeds of both PMDs are greater than 15 km/h.

Speed (km/h)

15 50
40
30
20 10 0 5 10 60
20 25
70

Cumulative Frequency

30
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No. of Hours, t Cumulative Frequency

2t 8 4t 18 6t 34
8t 55
10t 74
12t 89
14t 100
(i) Construct a frequency table for the given data. (ii) Using yours answer in (i), draw a histogram to represent the frequency distribution in the grid below. (iii) Determine (a) the modal class, (b) the percentage of students who spend more than 6 hours a week on social media, (c) the percentage of students who spend more than 4 but less than or equal to 10 hours a week on social media, (d) the mean amount of time spent on social media. www.jimmymaths.com

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 VKRZQ LQWKHFXPXODWLYHIUHTXHQF\FXUYHEHORZ (i) Assuming each family was only surveyed once, how many families were involved? (ii) Use the curve to estimate (a) the number of families who watch 15 hours or less a week, (b) the percentage of families who watch more than 35 hours a week, (c) the value of x, if 30% of families watch x hours or less a week. (iii) A family is randomly selected from the group. Find the probability that they watch (a) equal to or less than x hours a week, (b) more than 25 hours a week, (c) more than 20 hours but less than or equal to 30 hours a week.

Cumulative

Frequency

Time (h)

250
200
150
100
50
0 0 10 300
20 30
40
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VKRZVWKHLUPDUNVPDUNV7KH KLJKHVWSRVVLEOHPDUNLV From the graph, estimate (a) the number of students who scored less than 100 marks, (b) the number of students who scored at least 60 but less than 100 marks, (c) the value of b, such that 60% of the students scored less than b marks, (d) what the pass mark should be, if the examination board wants 80% of students to pass the examination.

Marks

120
50
40
30
20 10 0 20 40
60
80

Cumulative Frequency

100
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IROORZLQJFXPXODWLYHIUHTXHQF\FXUYHV (i) For both Boys and Girls, use the graphs to estimate (a) the number of Girls who are less than or equal to 145 cm, (b) the number of Boys who are taller than 160 cm, (c) the number of students who are taller than 150 cm. (ii) What is the gender of the tallest person in the school whose height was measured, and what is his/her height?

Height (cm)

150
100
80
60
40
20 0 130
140
120
160
170
140

Cumulative Frequency

180

Girls

Boys www.jimmymaths.com

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DQGDWOHDVWPDUNVWRJHWDGLVWLQFWLRQ (i) For both Class A and B, use the graphs to estimate (a) the number of students from Class A who passed the test, (b) the total number of students that attained a distinction, (ii) What was the highest mark attained, and which class was that student from? (iii) A student is randomly selected. Find the probability that (a) he/she is from Class A who attained a distinction. (b) he/she is from Class B who failed the test. (c) he/she got at least 60 but less than 70 marks for the test. 60
50
40
30
20 10 0 20 40
80
100

Cumulative Frequency

Marks

Class A

Class B

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(iv) Later in the year, students from Class A took another test and the cumulative frequency curve for the second test was plot against the results of their first test.

The curves are as shown below:

Which was a more difficult paper for students? Explain your answer. 60
50
40
30
20 10 0 20 40
80
100

Cumulative Frequency

Marks

Test 1

Test 2

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 RI PLOOLRQ6LQJDSRUHDQVIURPWKH\HDU (i) Using the graph (a) estimate the percentage of the population who earn less than or equal to $4000 a month, (b) estimate the value of x, such that 50% of Singaporeans earned at least $x or less. (c) hence, calculate how much the highest earning Singaporean earns a month as a percentage of $x.

Monthly Income ($)

12000

1 0.8 0.6 0.4 0.2 0 2000
4000
6000
8000

Cumulative Frequency

(in millions)

10000

14000

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(ii) Using the data above, complete the frequency distribution table below. Monthly Income Range ($x) Number of People (millions)

0 1000x

1000 1500x

1500 2000x

2000 2500x

2500 3000x

3000 4000x

4000 6000x

6000 13600x

(iii) Using the table, find an estimate of the mean Singaporean income. www.jimmymaths.com

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Cumulative Frequency

Marks (x)

30
40
20 10 0 10 20 30
40
50