Question 17
Pooja collected data on the number of tickets sold at the Bhopal railway station for a few different cities of Madhya Pradesh over a two-hour period.
She used this data and prepared a bar graph on the board to discuss the data with her students, but someone erased a portion of the graph.
a. Write the number of tickets sold for Vidisha above the bar. b. Write the number of tickets sold for Jabalpur above the bar. c. The bar for Vidisha is 6 unit lengths and the bar for Jabalpur is 5 unit lengths. What is the scale for this graph? d. Draw the correct bar for Sagar. e. Add the scale of the bar graph by placing the correct numbers on the vertical axis. f. Are the bars for Seoni and Indore correct in this graph? If not, draw the correct bar(s).
We need to use the given table to complete a bar graph.
Step 1 — Understand the Data
The table shows tickets sold for different cities. Look at the table above. It lists five cities. It shows the number of tickets for each city. Vidisha has 24 tickets. Jabalpur has 20 tickets. Seoni has 16 tickets. Indore has 28 tickets. Sagar has 16 tickets.
Step 2 — Find the Graph Scale
We are told about Vidisha's bar. Vidisha's bar is 6 unit lengths tall. Vidisha has 24 tickets. Let us find how many tickets each unit length stands for. We divide the total tickets by the bar length.
We can check this with Jabalpur. Jabalpur's bar is 5 unit lengths tall. Jabalpur has 20 tickets.
Both calculations give the same scale. So, 1 unit length on the graph means 4 tickets.
Step 3 — Annotate Vidisha and Jabalpur Bars
For part (a), we write the number of tickets for Vidisha. Vidisha has 24 tickets. We write 24 above the bar for Vidisha.
For part (b), we write the number of tickets for Jabalpur. Jabalpur has 20 tickets. We write 20 above the bar for Jabalpur.
Step 4 — Draw Sagar's Bar
For part (d), we need to draw the bar for Sagar. Sagar has 16 tickets. We know 1 unit length means 4 tickets. To find the bar length for Sagar, we divide tickets by the scale.
The bar for Sagar should be 4 unit lengths tall. We draw a bar of 4 unit lengths height for Sagar.
Step 5 — Label the Vertical Axis
For part (e), we add numbers to the vertical axis. The vertical axis shows the number of tickets. Each unit length is 4 tickets. So, the vertical axis should be marked like this: The first mark above 0 is 4. The next mark is 8. Then 12, 16, 20, 24, 28, and so on. We place these numbers at the correct unit length marks.
Step 6 — Check Seoni and Indore Bars
For part (f), we check Seoni and Indore bars. First, let us find the correct bar length for Seoni. Seoni has 16 tickets. We divide tickets by the scale.
So, the bar for Seoni should be 4 unit lengths tall.
Next, let us find the correct bar length for Indore. Indore has 28 tickets. We divide tickets by the scale.
So, the bar for Indore should be 7 unit lengths tall. We compare these calculated lengths to the bars on the graph. If the bars on the graph are not 4 unit lengths for Seoni and 7 unit lengths for Indore, then they are not correct. We draw the bars to these correct heights if they are wrong.
Answer
(a) Write 24 above the bar for Vidisha. (b) Write 20 above the bar for Jabalpur. (c) The scale for this graph is 1 unit length = 4 tickets. (d) Draw the bar for Sagar to a height of 4 unit lengths. (e) Label the vertical axis with numbers 0, 4, 8, 12, 16, 20, 24, 28, ... at each unit length mark. (f) The bar for Seoni should be 4 unit lengths tall. The bar for Indore should be 7 unit lengths tall. If the existing bars are different, draw them to these correct heights.
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