Interpret Grouped Frequency Tables

Question 1 of 6

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

8

$8$ hour period. How many buses had less than

20

$20$ passengers?

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

(37) $buses$ $\text(buses)$

Question 2 of 6

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

8

$8$ hour period. Find the modal class.

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

$Modal Class =$ $\text(Modal Class )=$ (10) $-$ $-$ (14)

Question 3 of 6

A bus depot conducted a survey on how many passengers were on each bus through an $8$ $8$ hour period. Find the mean.

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

Round off your answer to one decimal place.

$Mean =$ $\text(Mean )=$ (13.2)

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Mean Formula

Mean = \frac{\sum f \cdot c . c .}{\sum f}

$\text{Mean}=\frac{\color{#314EC4}{\sum f⋅c.c.}}{\color{#9202AA}{\sum f}}$

Remember

A grouped frequency distribution table is used for larger data sets and uses classes with intervals to group the scores.

First, find the sum of both the Frequency and $f \cdot c . c .$ $f⋅c.c.$ columns.

$\sum f$ $sum f$	$=$ $=$	$5 + 9 + 13 + 10 + 7 + 2$ $5+9+13+10+7+2$
	$=$ $=$	$46$ $46$

$\sum f \cdot x$ $sum f⋅x$	$=$ $=$	$10 + 63 + 156 + 170 + 154 + 54$ $10+63+156+170+154+54$
	$=$ $=$	$607$ $607$

Class	Class Centre $(c . c .)$ $(c.c.)$	Frequency $(f)$ $(f)$	$f \cdot c . c$ $f⋅c.c$
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
		$Total = 46$ $\text(Total) =46$	$Total = 607$ $\text(Total) =607$

Finally, use the formula to compute for the mean.

$Mean$ $\text(Mean)$	$=$ $=$	$\frac{\color{#314EC4}{\sum f⋅c.c.}}{\color{#9202AA}{\sum f}}$	Mean Formula

$Mean$ $\text(Mean)$	$=$ $=$	$\frac{\color{#314EC4}{607}}{\color{#9202AA}{46}}$	Substitute values

$Mean$ $\text(Mean)$	$=$ $=$	$13.2$ $13.2$	Rounded to one decimal place

Mean = 13.2

$\text(Mean)=13.2$

Question 4 of 6

The mass of

32

$32$ students was measured and the results are shown. Complete the grouped frequency distribution table and find the mean.

Class	Class Centre $(c . c .)$ $(c.c.)$	Frequency $(f)$ $(f)$
51-55	53	1
56-60	58	4
61-65	63	8
66-70	68	10
71-75	73	6
76-80	78	2
81-85	83	1
		$Total = 32$ $\text(Total) =32$

Round off your answer to one decimal place.

$Mean =$ $\text(Mean )=$ (67.1)

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Mean Formula

Mean = \frac{\sum f \cdot c . c .}{\sum f}

$\text{Mean}=\frac{\color{#314EC4}{\sum f⋅c.c.}}{\color{#9202AA}{\sum f}}$

Remember

A grouped frequency distribution table is used for larger data sets and uses classes with intervals to group the scores.

First, to complete the table, fill in the $f \cdot c . c$ $f⋅c.c$ column by multiplying $f$ $f$ and $c . c .$ $c.c.$ on each row.

Class	Class Centre $(c . c .)$ $(c.c.)$	Frequency $(f)$ $(f)$	$f \cdot c . c$ $f⋅c.c$
51-55	53	1	53
56-60	58	4	232
61-65	63	8	504
66-70	68	10	680
71-75	73	6	438
76-80	78	2	156
81-85	83	1	83
		$Total = 32$ $\text(Total) =32$

Next, find the sum of $f \cdot c . c .$ $f⋅c.c.$ column.

$\sum f \cdot x$ $sum f⋅x$	$=$ $=$	$53 + 232 + 504 + 680 + 438 + 156 + 83$ $53+232+504+680+438+156+83$
	$=$ $=$	$2146$ $2146$

Class	Class Centre $(c . c .)$ $(c.c.)$	Frequency $(f)$ $(f)$	$f \cdot c . c$ $f⋅c.c$
51-55	53	1	53
56-60	58	4	232
61-65	63	8	504
66-70	68	10	680
71-75	73	6	438
76-80	78	2	156
81-85	83	1	83
		$Total = 32$ $\text(Total) =32$	$Total = 2146$ $\text(Total) =2146$

Finally, use the formula to compute for the mean.

$Mean$ $\text(Mean)$	$=$ $=$	$\frac{\color{#314EC4}{\sum f⋅c.c.}}{\color{#9202AA}{\sum f}}$	Mean Formula

$Mean$ $\text(Mean)$	$=$ $=$	$\frac{\color{#314EC4}{2146}}{\color{#9202AA}{32}}$	Substitute values

$Mean$ $\text(Mean)$	$=$ $=$	$67.1$ $67.1$	Rounded to one decimal place

Mean = 67.1

$\text(Mean)=67.1$

Question 5 of 6

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

8

$8$ hour period. Find the median class.

$Class$ $\text(Class)$	$Class Centre (c . c .)$ $\text(Class Centre) (c.c.)$	$Frequency (f)$ $\text(Frequency) (f)$
$0 - 4$ $0-4$	$2$ $2$	$5$ $5$
$5 - 9$ $5-9$	$7$ $7$	$9$ $9$
$10 - 14$ $10-14$	$12$ $12$	$13$ $13$
$15 - 19$ $15-19$	$17$ $17$	$10$ $10$
$20 - 24$ $20-24$	$22$ $22$	$7$ $7$
$25 - 29$ $25-29$	$27$ $27$	$2$ $2$
		$Total = 46$ $\text(Total) =46$

$Median Class =$ $\text(Median Class )=$ (10)- (14)

Class	Class Centre $(c . c .)$ $(c.c.)$	Frequency $(f)$ $(f)$	Cumulative Frequency
0-4	2	5	5
5-9	7	9	5+9=14
10-14	12	13	14+13=27
15-19	17	10	27+10=37
20-24	22	7	37+7=44
25-29	27	2	44+2=46
		$Total = 46$ $\text(Total) =46$

Class	Class Centre $(c . c .)$ $(c.c.)$	Frequency $(f)$ $(f)$	Cumulative Frequency
0-4	2	5	5
5-9	7	9	5+9=14
10-14	12	13	14+13=27
15-19	17	10	27+10=37
20-24	22	7	37+7=44
25-29	27	2	44+2=46
		$Total = 46$ $\text(Total) =46$

Question 6 of 6

The mass of

32

$32$ students was measured and the results are shown. Find the median class.

$Class$ $\text(Class)$	$Class Centre (c . c .)$ $\text(Class Centre) (c.c.)$	$Frequency (f)$ $\text(Frequency) (f)$
$51 - 55$ $51-55$	$53$ $53$	$1$ $1$
$56 - 60$ $56-60$	$58$ $58$	$4$ $4$
$61 - 65$ $61-65$	$63$ $63$	$8$ $8$
$66 - 70$ $66-70$	$68$ $68$	$10$ $10$
$71 - 75$ $71-75$	$73$ $73$	$6$ $6$
$76 - 80$ $76-80$	$78$ $78$	$2$ $2$
$81 - 85$ $81-85$	$83$ $83$	$1$ $1$
		$Total = 32$ $\text(Total) =32$

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

$Total Buses$ $\text(Total Buses)$	$=$ $=$	$5 + 9 + 13 + 10$ $5+9+13+10$
	$=$ $=$	$37$ $37$

Interpret Grouped Frequency Tables

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Quiz summary

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1. Question

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Well Done!

2. Question

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Nice Job!

3. Question

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Excellent!

Mean Formula

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4. Question

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Mean Formula

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5. Question

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6. Question

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Quizzes

Class	Class Centre $(c . c .)$ $(c.c.)$	Frequency $(f)$ $(f)$	Cumulative Frequency
51-55	53	1	1
56-60	58	4	1+4=5
61-65	63	8	5+8=13
66-70	68	10	13+10=23
71-75	73	6	23+6=29
76-80	78	2	29+2=31
81-85	83	1	31+1=32
		$Total = 32$ $\text(Total) =32$