Question

The bar graph below shows Andrew's income and expenditure for each month from January to March.

Determine whether his total income in the three months was greater than his total expenditure for the same period.

Accepted Answer

The double bar graph below showing Andrew's income and expenditure for each month from January to March is given below.

The given double bar graph is a vertical bar graph.

The double (or group) bar graph allows a direct comparison of different sets of data within each class.

The height or length of the bar represents the number of observations or frequencies in that class or type of data and is proportional to the frequency of the class or data it represents. The greater the frequency of the class, the greater will be the length or height of the bar. In a bar graph, the bars should have equal width and the gaps between the bars should be uniform.

Now, we shall compute the income and the expenditure for the all the three month as follows:

$10$ smallest divisions along the vertical scale represent $₹ 10000$ .

So, $1$ smallest division along the vertical scale represents $\frac{₹ 10000}{10} = ₹ 1000$ .

Hence, the income for the month of January $= ₹ 20000 +$ income represented by $3$ smallest division $= ₹ 20000 + 3 \times (₹ 1000) = ₹ 20000 + ₹ 3000 = ₹ 23000$ .

And, the expenditure for the month of January $= ₹ 20000 +$ expenditure represented by $8$ smallest division $= ₹ 20000 + 8 \times (₹ 1000) = ₹ 20000 + ₹ 8000 = ₹ 28000 .$

The income for the month of February $= ₹ 20000 +$ income represented by $5$ smallest division $= ₹ 20000 + 5 \times (₹ 1000) = ₹ 20000 + ₹ 5000 = ₹ 25000$ .

And, the expenditure for the month of February $= ₹ 20000 +$ expenditure represented by $5$ smallest division $= ₹ 20000 + 5 \times (₹ 1000) = ₹ 20000 + ₹ 5000 = ₹ 25000$ .

The income for the month of March $= ₹ 20000 +$ income represented by $9$ smallest division $= ₹ 20000 + 9 \times (₹ 1000) = ₹ 20000 + ₹ 9000 = ₹ 29000$ .

And, the expenditure for the month of March $= ₹ 20000$ .

Now, the total income for the three months $= ₹ 23000 + ₹ 25000 + ₹ 29000 = ₹ 77000$ .

And, the total expenditure for the three months $= ₹ 28000 + ₹ 25000 + ₹ 20000 = ₹ 73000$ .

$₹ 77000$ is greater than $₹ 73000$ .

Therefore, yes, Andrew's total income in the three months was greater than his total expenditure for the same period.

Area in $9$	Frequency
$30 - 50$	$9$
$50 - 70$	$15$
$70 - 90$	$10$
$90 - 110$	$7$
$110 - 130$	$5$
$130 - 150$	$4$

Time in minutes	Frequency
$25 - 30$	$5$
$30 - 35$	$6$
_____	_____
$40 - 45$	$24$
$45 - 50$	$35$
$50 - 55$	$26$
$55 - 60$	$14$

Time in minutes	Frequency
$25 - 30$	$5$
$30 - 35$	$6$
_____	_____
$40 - 45$	$24$
$45 - 50$	$35$
$50 - 55$	$26$
$55 - 60$	$14$

Preferred Snack Choices of Students at Sujata's School
	Boys	Girls
Candy	$76$	$84$
Chips	$178$	$95$
Chocolate bars	$140$	$118$
Cookies	$72$	$92$
Fruit	$64$	$146$
Ice cream	$90$	$105$
Popcorn	$80$	$80$
Pastry	$100$	$80$

Preferred Snack Choices of Students at Sujata's School
	Boys	Girls
Candy	$76$	$84$
Chips	$178$	$95$
Chocolate bars	$140$	$118$
Cookies	$72$	$92$
Fruit	$64$	$146$
Ice cream	$90$	$105$
Popcorn	$80$	$80$
Pastry	$100$	$80$

Vistor Chow wal keung and RC Yadav Solutions for Chapter: Data Handling and Graphs, Exercise 6: EXERCISE

Vistor Chow wal keung Mathematics Solutions for Exercise - Vistor Chow wal keung and RC Yadav Solutions for Chapter: Data Handling and Graphs, Exercise 6: EXERCISE

Questions from Vistor Chow wal keung and RC Yadav Solutions for Chapter: Data Handling and Graphs, Exercise 6: EXERCISE with Hints & Solutions

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Transportation expenses (in $₹$ )	Frequency
$30 - 40$	$7$
$40 - 50$	$15$
$50 - 60$	$21$
$60 - 70$	$11$
$70 - 80$	$6$