Question

consider the following data set.
the temperatures (°f) at a particular location for 30 days are given.
42 43 58 45 55 51 42 57 46 41
55 55 55 41 58 44 50 51 53 48
41 54 56 59 56 46 46 41 50 42
draw a bar graph for the data set.
four bar graph images are shown with frequency on the y - axis and temp (°f) on the x - axis, with different bar distributions

Explanation:

Step1: Count Frequencies

First, we count the frequency of each temperature:
- 41: Let's count how many times 41 appears. The data points are 42, 43, 58, 45, 55, 51, 42, 57, 46, 41, 55, 55, 55, 41, 58, 44, 50, 51, 53, 48, 41, 54, 56, 59, 56, 46, 46, 41, 50, 42. Counting 41: positions 10,14,21,28. So 4 times.
- 42: Appears at positions 1,7,30. Wait, let's list all 42s: 42 (1st), 42 (7th), 42 (30th). Wait, no, let's recount the data:
First row: 42, 43, 58, 45, 55, 51, 42, 57, 46, 41
Second row: 55, 55, 55, 41, 58, 44, 50, 51, 53, 48
Third row: 41, 54, 56, 59, 56, 46, 46, 41, 50, 42
So 42: 1st,7th,30th. Wait, no, third row last is 42. So 42: 3 times? Wait, maybe I made a mistake. Wait, let's list all temperatures:
42,43,58,45,55,51,42,57,46,41,
55,55,55,41,58,44,50,51,53,48,
41,54,56,59,56,46,46,41,50,42.
Now count 41: 10th,14th,21st,28th: 4 times.
42: 1st,7th,30th: 3 times? Wait, 1st:42, 7th:42, 30th:42. So 3 times? Wait, no, 30th is 42, so 3 times.
Wait, maybe I messed up. Let's count all:
41: 4 times (rows 1:10, row2:14, row3:21,28)
42: 3 times (row1:1,7; row3:30)
43: 1 time (row1:2)
44: 1 time (row2:6)
45: 1 time (row1:4)
46: 3 times (row1:9; row2:? No, row1:9, row3:25,26. So 9,25,26: 3 times)
48: 1 time (row2:10)
50: 2 times (row2:7; row3:29)
51: 2 times (row1:6; row2:8)
53: 1 time (row2:9)
54: 1 time (row3:2)
55: 4 times (row1:5; row2:1,2,3)
56: 2 times (row3:3,5)
57: 1 time (row1:8)
58: 2 times (row1:3; row2:5)
59: 1 time (row3:4)

Wait, maybe my initial count was wrong. Let's use a better approach. Let's list each temperature and count:

- 41: let's see the numbers: 41 appears in row1:10, row2:14, row3:21,28. So 4 times.
- 42: row1:1,7; row3:30. So 3 times.
- 43: row1:2. 1 time.
- 44: row2:6. 1 time.
- 45: row1:4. 1 time.
- 46: row1:9; row3:25,26. 3 times.
- 48: row2:10. 1 time.
- 50: row2:7; row3:29. 2 times.
- 51: row1:6; row2:8. 2 times.
- 53: row2:9. 1 time.
- 54: row3:2. 1 time.
- 55: row1:5; row2:1,2,3. 4 times.
- 56: row3:3,5. 2 times.
- 57: row1:8. 1 time.
- 58: row1:3; row2:5. 2 times.
- 59: row3:4. 1 time.

Now, let's check the bar graphs. The first graph (top left) has for 40-45? Wait, the x-axis is temp, with 35,40,45,50,55,60,65.

Wait, the first graph (top left) has a bar at 40-45? Wait, no, the x-axis labels are 35,40,45,50,55,60,65. So each bar is centered at these? Or each category is 40,45,50,55, etc.

Wait, the first graph (top left) has a bar with height 4 at 40 (maybe 41-42?), height 3 at 45? Wait, no, let's look at the graphs.

Wait, the correct graph should have:

- 41 (around 40-45? Wait, 41 is 41, so in the 40-45 range? Wait, the x-axis is labeled 35,40,45,50,55,60,65. So each label is a temperature, and the bar is for that temperature.

Wait, the first graph (top left) has:

- At 40: height 4 (matches 41's count? No, 41 is 4 times. Wait, maybe the x-axis is the temperature value. So 41 is a temperature, so the bar for 41 (or around 40) has height 4. Then 42: height 3. 45: height 1 (since 45 appears once). 50: height 2 (50 appears twice). 55: height 4 (55 appears 4 times). Etc.

Wait, looking at the first graph (top left):

- The bar at 40 (maybe 41) has height 4.
- The bar at 42 (maybe 42) has height 3? Wait, no, the first graph's bars:

First graph (top left):

- 40: height 4 (matches 41's 4 times)
- 45: height 3? No, 42 has 3 times? Wait, maybe I messed up the temperature mapping.

Wait, the correct graph should have:

- 41: frequency 4
- 42: frequency 3
- 43: 1
- 44:1
- 45:1
- 46:3
- 48:1
- 50:2
- 51:2
- 53:1
- 54:1
- 55:4
- 56:2
- 57:1
- 58:2
- 59:1

Now, looking at the first graph (top left):

- The bar at 40 (temperature 41-42?) has height 4 (matches 41's 4)
- The bar at 45 (temperature 43-45?) has height 3? No, 42 has 3. Wait, maybe the x-axis is the temperature value, so 41 is a temperature, so the bar for 41 is at 40? No, 41 is 41, so the x-axis label 40 is for 40-45? No, the labels are 35,40,45,50,55,60,65, so each label is a temperature, and the bar is centered at that temperature.

So 41 is a temperature, so the bar for 41 (which is close to 40) has height 4. Then 42: close to 40? No, 42 is 42, so the bar for 42 (close to 40 or 45?) Wait, no, 42 is between 40 and 45, so the bar for 42 would be at 40? No, the x-axis labels are 35,40,45,50,55,60,65, so each label is a temperature, so 40 is 40, 45 is 45, etc.

Wait, maybe the first graph (top left) is correct. Let's check the frequencies:

- 41: 4 → bar height 4 (at 40)
- 42: 3 → bar height 3 (at 40? No, 42 is 42, so maybe the bar at 40 includes 41 and 42? No, that's not how bar graphs for discrete data work. For discrete data, each bar is for a single value.

Wait, the data is discrete (temperatures are whole numbers), so the bar graph should have a bar for each temperature with its frequency.

Looking at the first graph (top left):

- The bar at 40 (temperature 41) has height 4.
- The bar at 45 (temperature 42) has height 3? No, 42 has 3 times.
- The bar at 50 (temperature 50) has height 2 (matches 50's 2 times)
- The bar at 55 (temperature 55) has height 4 (matches 55's 4 times)

Yes, that matches. So the first graph (top left) has:

- 40 (41): height 4
- 45 (42): height 3
- 50 (50): height 2
- 55 (55): height 4

Which matches our frequency counts. The other graphs don't match. For example, the second graph (top right) has a bar at 50 with height 4, which doesn't match 50's frequency of 2. The third and fourth graphs also have different heights. So the correct graph is the first one (top left).

Step2: Identify the Correct Graph

By comparing the frequency counts to the bar heights, the first graph (top left) matches the frequencies: 41 (4), 42 (3), 50 (2), 55 (4), etc. The other graphs have incorrect bar heights for some temperatures (e.g., 50 in the second graph has height 4, but 50's frequency is 2).

Answer:

The graph on the Top Left