Question

ann created a histogram based on this data set from her lab partner: 4.1, 4.3, 4.3, 4.5, 4.6, 4.6, 4.8, 5.0, 5.5, 5.7, 5.7, 5.8, 5.8, 6.6. she used the ranges 4.0–4.4, 4.5–4.9, 5.0–5.4, 5.5–5.9, 6.0–6.4, and 6.5–6.9. later, ann’s lab partner said the two 5.8 measurements were supposed to be 6.2 and 6.5. ann updated her histogram accordingly. for which ranges did she have to change the frequencies? select all that apply. 4.0–4.4, 4.5–4.9, 5.0–5.4, 5.5–5.9, 6.0–6.4, 6.5–6.9

Explanation:

Step1: Analyze each range

First, list the data set: 4.1, 4.3, 4.3, 4.5, 4.6, 4.6, 4.8, 5.0, 5.0, 5.5, 5.7, 5.7, 5.8, 5.8, 6.6. Then check each range:

- **4.0 - 4.4**: Data points here are 4.1, 4.3, 4.3. No new data (6.2, 6.5) in this range, so no change.
- **4.5 - 4.9**: Data points here are 4.5, 4.6, 4.6, 4.8. No new data in this range, so no change.
- **5.0 - 5.4**: Data points here are 5.0, 5.0. No new data (6.2, 6.5) in this range, so no change.
- **5.5 - 5.9**: Original data points: 5.5, 5.7, 5.7, 5.8, 5.8. No new data (6.2, 6.5) in this range, so no change? Wait, no, wait the new data is 6.2 and 6.5. Wait, let's re - check the ranges and new data. The new data is 6.2 and 6.5.
- **6.0 - 6.4**: Original data in this range: none (since the original data's highest below 6.5 is 5.8). Now new data 6.2 is in this range. So this range's frequency will change.
- **6.5 - 6.9**: Original data in this range: none (original data has 6.6? Wait, wait the original data set: wait the user's data set: wait the original data given is "4.1, 4.3, 4.3, 4.5, 4.6, 4.6, 4.8, 5.0, 5.0, 5.5, 5.7, 5.7, 5.8, 5.8, 6.6". Oh! I missed 6.6 earlier. So original data in 6.5 - 6.9: 6.6. Now new data 6.5 is added? Wait, the new data is 6.2 and 6.5. So:

For range 6.0 - 6.4: new data 6.2 is added (original had no data in 6.0 - 6.4? Wait original data: 6.6 is in 6.5 - 6.9. So 6.0 - 6.4: original data points: none. Now 6.2 is added. So frequency changes.

For range 6.5 - 6.9: original data point: 6.6. Now new data 6.5 is added. So frequency changes.

Wait, let's re - list all data including new (6.2, 6.5) and original:

Original data: 4.1, 4.3, 4.3, 4.5, 4.6, 4.6, 4.8, 5.0, 5.0, 5.5, 5.7, 5.7, 5.8, 5.8, 6.6

New data: 6.2, 6.5

Now check each range:

1. 4.0 - 4.4: 4.1, 4.3, 4.3 (no new data here)
2. 4.5 - 4.9: 4.5, 4.6, 4.6, 4.8 (no new data here)
3. 5.0 - 5.4: 5.0, 5.0 (no new data here)
4. 5.5 - 5.9: 5.5, 5.7, 5.7, 5.8, 5.8 (no new data here)
5. 6.0 - 6.4: Original: none. New: 6.2. So frequency changes.
6. 6.5 - 6.9: Original: 6.6. New: 6.5. So frequency changes.

Step2: Confirm the ranges with changed frequencies

So the ranges where frequencies change are 6.0 - 6.4 and 6.5 - 6.9. Wait, but let's check again. Wait the original data set: when Ann first made the histogram, the data was the original set (without 6.2 and 6.5). Then the lab partner said the two measurements were 6.2 and 6.5. So we need to see which ranges these new data points fall into.

6.2 falls into 6.0 - 6.4.

6.5 falls into 6.5 - 6.9.

Now, let's check the original frequency for 6.0 - 6.4: original data has no values in 6.0 - 6.4 (since the original data's values are up to 6.6, but 6.6 is in 6.5 - 6.9). So when we add 6.2, the frequency of 6.0 - 6.4 goes from 0 to 1.

For 6.5 - 6.9: original data has 6.6. Now we add 6.5, so the frequency increases by 1.

Now, what about the other ranges? Let's check 5.5 - 5.9: original data has 5.5, 5.7, 5.7, 5.8, 5.8. No new data here. 5.0 - 5.4: original has 5.0, 5.0. No new data. 4.5 - 4.9: original has 4.5, 4.6, 4.6, 4.8. No new data. 4.0 - 4.4: original has 4.1, 4.3, 4.3. No new data.

Wait, but maybe I made a mistake earlier. Let's re - list the original data set as per the image: the data set is 4.1, 4.3, 4.3, 4.5, 4.6, 4.6, 4.8, 5.0, 5.0, 5.5, 5.7, 5.7, 5.8, 5.8, 6.6. Then the new data is 6.2 and 6.5.

So 6.2 is in 6.0 - 6.4, 6.5 is in 6.5 - 6.9.

Now, let's check the range 5.5 - 5.9 again. The new data (6.2, 6.5) are not in 5.5 - 5.9. So 5.5 - 5.9's frequency remains the same.

So the ranges that need to have their frequencies changed are 6.0 - 6.4 and 6.5 - 6.9. Wait, but let's check the options. The options are 4.0 - 4.4, 4.5 - 4.9, 5.0 - 5.4, 5.5 - 5.9, 6.0 - 6.4, 6.5 - 6.9.

Wait, maybe I missed that 6.6 is in 6.5 - 6.9. So original frequency for 6.5 - 6.9: 1 (for 6.6). Now with 6.5, it becomes 2.

For 6.0 - 6.4: original frequency 0, now 1 (for 6.2).

Now, are there any other ranges? Let's check 5.0 - 5.4: data is 5.0, 5.0. No new data. 4.5 - 4.9: data is 4.5, 4.6, 4.6, 4.8. No new data. 4.0 - 4.4: data is 4.1, 4.3, 4.3. No new data. 5.5 - 5.9: data is 5.5, 5.7, 5.7, 5.8, 5.8. No new data.

So the ranges with changed frequencies are 6.0 - 6.4 and 6.5 - 6.9.

Answer:

6.0 - 6.4, 6.5 - 6.9