Create Grouped Frequency Tables and Graphs

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Question 1 of 8

Shown are the ages of

$48$ people who belong to a tennis club. Organise the data into a grouped frequency distribution table. Use the class intervals displayed in the table.

$18$	$13$	$16$	$20$	$37$	$40$	$39$	$42$
$12$	$15$	$27$	$20$	$16$	$18$	$33$	$40$
$29$	$34$	$41$	$27$	$19$	$12$	$44$	$13$
$38$	$43$	$22$	$17$	$35$	$30$	$19$	$26$
$25$	$43$	$33$	$18$	$23$	$35$	$41$	$32$
$28$	$11$	$28$	$21$	$35$	$19$	$41$	$28$

Enter the frequency for each respective score in the table below

Class Frequency $(f)$

10-15 (6)

16-20 (11)

21-25 (4)

26-30 (8)

31-35 (7)

36-40 (5)

41-45 (7)

$\text(Total) =$

Question 2 of 8

2. Question
The scores of $36$ students in a history quiz out of 50 are given. Organise the data into a grouped frequency distribution table and find the modal class.

$43$ $35$ $27$ $34$ $36$ $44$ $29$ $35$ $43$

$50$ $35$ $22$ $21$ $29$ $42$ $32$ $20$ $32$

$31$ $41$ $37$ $30$ $39$ $38$ $40$ $39$ $23$

$41$ $33$ $37$ $36$ $35$ $29$ $50$ $30$ $42$

Use class intervals of $5$ , starting from $16-20$
- $\text(Modal Class )=$ (31) $-$ (35)
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A grouped frequency distribution table is used for larger data sets and uses classes with intervals to group the scores.

A modal class is the group of scores with the highest frequency.

Read across the data while placing a stroke in the Tally column for each corresponding score.

$43$ $35$ $27$ $34$ $36$ $44$ $29$ $35$ $43$

$50$ $35$ $22$ $21$ $29$ $42$ $32$ $20$ $32$

$31$ $41$ $37$ $30$ $39$ $38$ $40$ $39$ $23$

$41$ $33$ $37$ $36$ $35$ $29$ $50$ $30$ $42$

Class Tally Frequency $(f)$

16-20

21-25

26-30

31-35

36-40

41-45

46-50

Continue doing this until all scores are tallied.

Class Tally Frequency $(f)$

16-20

21-25

26-30

31-35

36-40

41-45

46-50

Count the tallies per score and note it under the Frequency column.

Class Tally Frequency $(f)$

16-20 1

21-25 3

26-30 6

31-35 9

36-40 8

41-45 7

46-50 2

To check, count the total frequency and make sure it is equal to the number of given scores.

Class Tally Frequency $(f)$

16-20 1

21-25 3

26-30 6

31-35 9

36-40 8

41-45 7

46-50 2

$\text(Total) =36$

From the given data, we know that $N=36$

Therefore, all scores have been accounted for.

Notice that the highest value in the Frequency column is $9$ and it corresponds to $31-35$ .

Class Tally Frequency $(f)$

16-20 1

21-25 3

26-30 6

31-35 9

36-40 8

41-45 7

46-50 2

$\text(Total) =36$

In other words, the class $31-35$ occurs the most frequently, and is therefore the modal class.

$\text(Modal Class)=31-35$
Question 3 of 8

3. Question
The mass of $32$ students was measured and the results are shown. Organise the data into a grouped frequency distribution table and find the modal class.

$71$ $52$ $66$ $64$ $82$ $78$ $61$ $72$

$73$ $68$ $70$ $62$ $77$ $56$ $65$ $68$

$61$ $74$ $57$ $71$ $71$ $58$ $63$ $60$

$68$ $70$ $68$ $69$ $68$ $65$ $68$ $62$

Use class intervals of $5$ , starting from $51-55$
- $\text(Modal Class )=$ (66) $-$ (70)
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A grouped frequency distribution table is used for larger data sets and uses classes with intervals to group the scores.

A modal class is the group of scores with the highest frequency.

Read across the data while placing a stroke in the Tally column for each corresponding score.

$71$ $52$ $66$ $64$ $82$ $78$ $61$ $72$

$73$ $68$ $70$ $62$ $77$ $56$ $65$ $68$

$61$ $74$ $57$ $71$ $71$ $58$ $63$ $60$

$68$ $70$ $68$ $69$ $68$ $65$ $68$ $62$

Class Tally Frequency $(f)$

51-55

56-60

61-65

66-70

71-75

76-80

81-85

Continue doing this until all scores are tallied.

Class Tally Frequency $(f)$

51-55

56-60

61-65

66-70

71-75

76-80

81-85

Count the tallies per score and note it under the Frequency column.

Class Tally Frequency $(f)$

51-55 1

56-60 4

61-65 8

66-70 10

71-75 6

76-80 2

81-85 1

To check, count the total frequency and make sure it is equal to the number of given scores.

Class Tally Frequency $(f)$

51-55 1

56-60 4

61-65 8

66-70 10

71-75 6

76-80 2

81-85 1

$\text(Total) =32$

From the given data, we know that $N=32$

Therefore, all scores have been accounted for.

Notice that the highest value in the Frequency column is $10$ and it corresponds to $66-70$ .

Class Tally Frequency $(f)$

51-55 1

56-60 4

61-65 8

66-70 10

71-75 6

76-80 2

81-85 1

$\text(Total) =32$

In other words, the class $66-70$ occurs the most frequently, and is therefore the modal class.

$\text(Modal Class)=66-70$

Class	Frequency $(f)$
10-15	(6)
16-20	(11)
21-25	(4)
26-30	(8)
31-35	(7)
36-40	(5)
41-45	(7)
	$\text(Total) =$

Class	Tally	Frequency $(f)$
10-15		6
16-20		11
21-25		4
26-30		8
31-35		7
36-40		5
41-45		7
		$\text(Total) =$

Class	Tally	Frequency $(f)$
10-15		6
16-20		11
21-25		4
26-30		8
31-35		7
36-40		5
41-45		7
		$\text(Total) =48$

Class	Tally	Frequency $(f)$
10-15		6
16-20		11
21-25		4
26-30		8
31-35		7
36-40		5
41-45		7
		$\text(Total) =48$

Question 4 of 8

A bus depot conducted a survey on how many passengers were on each bus through an

$8$ hour period. Complete the frequency distribution table.

Enter the value for each respective column in the table below

Class	Class Centre $(c.c.)$	Frequency $(f)$	$f⋅c.c.$
$0-4$	(2)	$5$	(10)
$5-9$	(7)	$9$	(63)
$10-14$	(12)	$13$	(156)
$15-19$	(17)	$10$	(170)
$20-24$	(22)	$7$	(154)
$25-29$	(27)	$2$	(54)

Class	Class Centre $(c.c.)$	Frequency $(f)$
0-4	2	5
5-9	7	9
10-14	12	13
15-19	17	10
20-24	22	7
25-29	27	2

Class	Class Centre $(c.c.)$	Frequency $(f)$	$f⋅c.c$
0-4	2	5	10
5-9	7	9	63
10-14	12	13	156
15-19	17	10	170
20-24	22	7	154
25-29	27	2	54

Class	Class Centre $(c.c.)$	Frequency $(f)$	$f⋅c.c$
0-4	2	5	10
5-9	7	9	63
10-14	12	13	156
15-19	17	10	170
20-24	22	7	154
25-29	27	2	54

Question 5 of 8

The scores of

$36$ students in a history quiz out of 50 are given. Complete the grouped frequency distribution table and create a histogram.

Class	Class Centre $(c.c.)$	Frequency $(f)$
16-20		1
21-25		3
26-30		6
31-35		9
36-40		8
41-45		7
46-50		2
		$\text(Total) =36$

Class	Class Centre $(c.c.)$	Frequency $(f)$
16-20	18	1
21-25	23	3
26-30	28	6
31-35	33	9
36-40	38	8
41-45	43	7
46-50	48	2
		$\text(Total) =36$

Class	Class Centre $(c.c.)$	Frequency $(f)$
16-20	18	1
21-25	23	3
26-30	28	6
31-35	33	9
36-40	38	8
41-45	43	7
46-50	48	2
		$\text(Total) =36$

Question 6 of 8

The mass of

$32$ students was measured and the results are shown. Complete the grouped frequency distribution table and create a histogram.

Class	Class Centre $(c.c.)$	Frequency $(f)$
51-55		1
56-60		4
61-65		8
66-70		10
71-75		6
76-80		2
81-85		1
		$\text(Total) =32$

Question 7 of 8

7. Question
The mass of $32$ students was measured and the results are shown. Draw a grouped frequency polygon.
- 1.
- 2.
- 3.
- 4.
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A frequency polygon is a line graph version of the frequency distribution table.

Create a cumulative frequency polygon by simply connecting the top-right corners of each bar using straight lines, as shown here.
Question 8 of 8

8. Question
The mass of $32$ students was measured and the results are shown. Find the median class by drawing a cumulative frequency histogram.

Class Class Centre $(c.c.)$ Cumulative
Frequency

51-55 53 1

56-60 58 5

61-65 63 13

66-70 68 23

71-75 73 29

76-80 78 31

81-85 83 32
- $\text(Median Class )=$ (66)- (70)
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The median is the middle value in an ordered set of data.

First, create a graph with the Class Centre $(c.c.)$ values on the bottom side and the Cumulative Frequency values on the left side.

Next, add bars to the graph corresponding to the cumulative frequency per class centre.

Class Class Centre $(c.c.)$ Cumulative Frequency

51-55 53 1

56-60 58 5

61-65 63 13

66-70 68 23

71-75 73 29

76-80 78 31

81-85 83 32

$\text(Total) =32$

Continue adding bars until all the scores are accounted for.

Next, find the middle value in the cumulative frequency axis (left side).

Since the highest value is $32$ , simply divide it by $2$ .

$32/2$ $=$ $16$

Trace a horizontal line from $16$ until it touches part of the polygon.

Notice that it touches the polygon across the bar for the class centre $68$ .

Hence, the median is the class $66-70$ .

$\text(Median Class)=66-70$

Create Grouped Frequency Tables and Graphs

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Quiz summary

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Quizzes

$18$	$13$	$16$	$20$	$37$	$40$	$39$	$42$
$12$	$15$	$27$	$20$	$16$	$18$	$33$	$40$
$29$	$34$	$41$	$27$	$19$	$12$	$44$	$13$
$38$	$43$	$22$	$17$	$35$	$30$	$19$	$26$
$25$	$43$	$33$	$18$	$23$	$35$	$41$	$32$
$28$	$11$	$28$	$21$	$35$	$19$	$41$	$28$

$43$	$35$	$27$	$34$	$36$	$44$	$29$	$35$	$43$
$50$	$35$	$22$	$21$	$29$	$42$	$32$	$20$	$32$
$31$	$41$	$37$	$30$	$39$	$38$	$40$	$39$	$23$
$41$	$33$	$37$	$36$	$35$	$29$	$50$	$30$	$42$

$71$	$52$	$66$	$64$	$82$	$78$	$61$	$72$
$73$	$68$	$70$	$62$	$77$	$56$	$65$	$68$
$61$	$74$	$57$	$71$	$71$	$58$	$63$	$60$
$68$	$70$	$68$	$69$	$68$	$65$	$68$	$62$

$71$	$52$	$66$	$64$	$82$	$78$	$61$	$72$
$73$	$68$	$70$	$62$	$77$	$56$	$65$	$68$
$61$	$74$	$57$	$71$	$71$	$58$	$63$	$60$
$68$	$70$	$68$	$69$	$68$	$65$	$68$	$62$

$\text(Mean (0-4))$	$=$	$(0+4)/2$

	$=$	$2$

$\text(Mean (5-9))$	$=$	$(5+9)/2$

	$=$	$7$

$\text(Mean (10-14))$	$=$	$(10+14)/2$

	$=$	$12$

$\text(Mean (15-19))$	$=$	$(15+19)/2$

	$=$	$17$

$\text(Mean (20-24))$	$=$	$(20+24)/2$

	$=$	$22$

$\text(Mean (25-29))$	$=$	$(25+29)/2$

	$=$	$27$

$\text(Mean (16-20))$	$=$	$(16+20)/2$

	$=$	$18$

$\text(Mean (21-25))$	$=$	$(21+25)/2$

	$=$	$23$

$\text(Mean (26-30))$	$=$	$(26+30)/2$

	$=$	$28$

$\text(Mean (31-35))$	$=$	$(31+35)/2$

	$=$	$33$

$\text(Mean (36-40))$	$=$	$(36+40)/2$

	$=$	$38$

$\text(Mean (41-45))$	$=$	$(41+45)/2$

	$=$	$43$

$\text(Mean (46-50))$	$=$	$(46+50)/2$

	$=$	$48$

$\text(Mean (51-55))$	$=$	$(51+55)/2$

	$=$	$53$

$\text(Mean (56-60))$	$=$	$(56+60)/2$

	$=$	$58$

$\text(Mean (61-65))$	$=$	$(61+65)/2$

	$=$	$63$

$\text(Mean (66-70))$	$=$	$(66+70)/2$

	$=$	$68$

$\text(Mean (71-75))$	$=$	$(71+75)/2$

	$=$	$73$

$\text(Mean (76-80))$	$=$	$(76+80)/2$

	$=$	$78$

$\text(Mean (81-85))$	$=$	$(81+85)/2$

	$=$	$83$