Question

below are ages (in years, rounded to the nearest tenth) of randomly selected attendees of a climate strike rally during the year of 2019.

8.1\t8.4\t9.3\t9.3\t9.5\t9.7\t9.8\t10.5
10.7\t11.2\t11.6\t11.7\t11.8\t11.9\t12.0\t12.1
12.4\t12.5\t12.6\t13.0\t13.6\t14.2\t14.4\t14.6
14.7\t14.8\t14.8\t14.9\t15.0\t15.4\t15.6\t16.4
17.9\t19.3\t19.4\t19.6\t19.8\t21.9\t22.8\t23.6

construct a frequency distribution table for this information using 8 classes. enter relative frequencies as well, rounded to three places after the decimal.

the first lower class limit should be the minimum value. the class width should be rounded up to the next tenths place.

hint 1 hint 2 hint 3

lower class limits\tupper class limits\tfrequency\trel. freq.
8.1 ✔️\t10.0 ✔️\t7 ✔️\t0.175 ✔️
10.1 ✔️\t12.0 ✔️\t8 ✔️\t0.200 ✔️
12.1 ✔️\t14.0 ✔️\t7 ❌\t0.167 ❌
14.1 ✔️\t16.0 ✔️\t11 ❌\t0.262 ❌
16.1 ✔️\t18.0 ✔️\t2 ✔️\t0.050 ✔️
18.1 ✔️\t20.0 ✔️\t4 ✔️\t0.100 ✔️

Explanation:

Step 1: Find the total number of data points

First, we count the number of ages. Let's list them:
Row 1: 8 (8.1, 8.4, 9.3, 9.3, 9.5, 9.7, 9.8, 10.5)
Row 2: 8 (10.7, 11.2, 11.6, 11.7, 11.8, 11.9, 12.0, 12.1)
Row 3: 8 (12.4, 12.5, 12.6, 13.0, 13.6, 14.2, 14.4, 14.6)
Row 4: 8 (14.7, 14.8, 14.8, 14.9, 15.0, 15.4, 15.6, 16.4)
Row 5: 8 (17.9, 19.3, 19.4, 19.6, 19.8, 21.9, 22.8, 23.6) Wait, no, row 5 has 6? Wait, original table: first row 8, second 8, third 8, fourth 8, fifth 6? Wait, let's count again:

First row: 8.1, 8.4, 9.3, 9.3, 9.5, 9.7, 9.8, 10.5 → 8
Second: 10.7, 11.2, 11.6, 11.7, 11.8, 11.9, 12.0, 12.1 → 8
Third: 12.4, 12.5, 12.6, 13.0, 13.6, 14.2, 14.4, 14.6 → 8
Fourth: 14.7, 14.8, 14.8, 14.9, 15.0, 15.4, 15.6, 16.4 → 8
Fifth: 17.9, 19.3, 19.4, 19.6, 19.8, 21.9, 22.8, 23.6 → Wait, no, the fifth row has 6? Wait, the original problem's table:

Looking at the given table:

Row 1: 8 entries
Row 2: 8
Row 3: 8
Row 4: 8
Row 5: 6? Wait, no, the user's image shows:

First row: 8.1, 8.4, 9.3, 9.3, 9.5, 9.7, 9.8, 10.5 → 8
Second: 10.7, 11.2, 11.6, 11.7, 11.8, 11.9, 12.0, 12.1 → 8
Third: 12.4, 12.5, 12.6, 13.0, 13.6, 14.2, 14.4, 14.6 → 8
Fourth: 14.7, 14.8, 14.8, 14.9, 15.0, 15.4, 15.6, 16.4 → 8
Fifth: 17.9, 19.3, 19.4, 19.6, 19.8, 21.9, 22.8, 23.6 → Wait, no, the fifth row has 8? Wait, 17.9, 19.3, 19.4, 19.6, 19.8, 21.9, 22.8, 23.6 → 8? Wait, 17.9 is one, then 19.3,19.4,19.6,19.8 (that's 5), then 21.9,22.8,23.6 (3) → total 8? Wait, 1+4+3=8? Yes. So total data points: 8*5=40? Wait, 8+8+8+8+8=40? Wait, no, first four rows 8 each, fifth row 8? Wait, let's count again:

Row 1: 8
Row 2: 8 (total 16)
Row 3: 8 (24)
Row 4: 8 (32)
Row 5: 8 (40). Yes, 40 data points.

Step 2: Determine Class Width

First, find the range: maximum - minimum. Minimum is 8.1, maximum is 23.6. Range = 23.6 - 8.1 = 15.5. Number of classes = 8. So class width = range / number of classes = 15.5 / 8 = 1.9375. Round up to the next tenths place: 2.0? Wait, no, the first class is 8.1 - 10.0 (width 1.9), but maybe the class width is calculated as (max - min)/n, then round up. Wait, the first class lower limit is 8.1, upper limit 10.0 (width 1.9). Then next class 10.1 - 12.0 (width 1.9), etc. So class width is 1.9, but rounded up to tenths: 2.0? Wait, no, 1.9375 rounded up to tenths is 2.0? Wait, 1.9375 is between 1.9 and 2.0. Rounding up to the next tenths place: 2.0? Wait, but the first class is 8.1 - 10.0 (width 1.9). Maybe the problem says "rounded up to the next tenths place" so 1.9375 rounded up to tenths is 2.0? Wait, no, 1.9375's tenths place is 9, the next tenths place is 2.0? Wait, maybe the class width is 2.0? Wait, but the first class is 8.1 - 10.0 (width 1.9). Maybe the initial calculation is (23.6 - 8.1)/8 = 15.5/8 = 1.9375, so we round up to 2.0? But the first class in the hint is 8.1 - 10.0 (width 1.9). Maybe the problem's class width is 1.9, but rounded up to tenths: 2.0? Wait, no, 1.9375 rounded up to the next tenths place: the tenths digit is 9, so the next tenths place is 2.0? Wait, maybe the class width is 2.0, but the first class is 8.1 - 10.0 (since 8.1 + 1.9 = 10.0). So class width is 1.9, but rounded up to tenths is 2.0? Maybe the problem has a typo, but let's proceed with the given classes.

Step 3: Count Frequencies for Each Class

Class 1: 8.1 - 10.0

Data points: 8.1, 8.4, 9.3, 9.3, 9.5, 9.7, 9.8, 10.5? Wait, 10.5 is above 10.0? Wait, 10.0 is upper limit. So 8.1, 8.4, 9.3, 9.3, 9.5, 9.7, 9.8: that's 7. Wait, 10.5 is in next class. So frequency 7 (correct as per hint).

Class 2: 10.1 - 12.0

Data points: 10.7, 11.2, 11.6, 11.7, 11.8, 11.9, 12.0, 10.5? Wait, 10.5 is 10.5, which is above 10.0, so 10.5 is in 10.1 - 12.0? Wait, 10.1 is lower limit, 12.0 upper. So 10.5, 10.7, 11.2, 11.6, 11.7, 11.8, 11.9, 12.0: that's 8 (correct as per hint).

Class 3: 12.1 - 14.0

Data points: 12.1, 12.4, 12.5, 12.6, 13.0, 13.6, 14.2? Wait, 14.2 is above 14.0. So 12.1, 12.4, 12.5, 12.6, 13.0, 13.6: that's 6? Wait, the hint has 7, which is wrong. Wait, let's list all data points in this range:

12.1 (yes), 12.4 (yes), 12.5 (yes), 12.6 (yes), 13.0 (yes), 13.6 (yes), 14.2? No, 14.2 is 14.2 >14.0. Wait, 14.0 is upper limit. So 12.1, 12.4, 12.5, 12.6, 13.0, 13.6: that's 6. Wait, maybe I missed one. Let's check row 2: 12.1 (yes). Row 3: 12.4,12.5,12.6,13.0,13.6. So that's 1 (row2) +5 (row3)=6. But hint has 7. Maybe 14.0 is included? Wait, 14.0 is in next class? No, next class is 14.1 -16.0. So 14.0 is in 12.1 -14.0. Wait, 14.0: is there a 14.0? No, the data points are 12.4,12.5,12.6,13.0,13.6,14.2,14.4,14.6 (row3). So 14.0 is not present. So frequency should be 6.

Class 4: 14.1 - 16.0

Data points: 14.2,14.4,14.6,14.7,14.8,14.8,14.9,15.0,15.4,15.6,16.4? Wait, 16.4 is above 16.0. So 14.2,14.4,14.6,14.7,14.8,14.8,14.9,15.0,15.4,15.6: that's 10. Wait, row3:14.2,14.4,14.6 (3), row4:14.7,14.8,14.8,14.9,15.0,15.4,15.6 (7). Total 3+7=10. But hint has 11, which is wrong.

Class 5: 16.1 - 18.0

Data points: 16.4? No, 16.4 is 16.4 >16.0, so 16.4 is in 16.1 -18.0? 16.1 is lower limit, 18.0 upper. So 16.4, 17.9: that's 2 (correct as per hint).

Class 6: 18.1 - 20.0

Data points: 19.3,19.4,19.6,19.8: that's 4 (correct as per hint).

Class 7: 20.1 - 22.0

Data points: 21.9: that's 1.

Class 8: 22.1 - 24.0

Data points: 22.8,23.6: that's 2.

Wait, but the problem says 8 classes. Let's recalculate the class limits with class width 2.0 (rounded up). Wait, maybe the initial class width calculation was wrong. Let's do it properly:

Range = 23.6 - 8.1 = 15.5

Number of classes = 8

Class width = 15.5 / 8 = 1.9375, so we round up to the next tenths place, which is 2.0. So class width is 2.0.

Then the classes would be:

1. 8.1 - 10.0 (8.1 + 2.0 - 0.1 = 10.0)
2. 10.1 - 12.0 (10.1 + 2.0 - 0.1 = 12.0)
3. 12.1 - 14.0 (12.1 + 2.0 - 0.1 = 14.0)
4. 14.1 - 16.0 (14.1 + 2.0 - 0.1 = 16.0)
5. 16.1 - 18.0 (16.1 + 2.0 - 0.1 = 18.0)
6. 18.1 - 20.0 (18.1 + 2.0 - 0.1 = 20.0)
7. 20.1 - 22.0 (20.1 + 2.0 - 0.1 = 22.0)
8. 22.1 - 24.0 (22.1 + 2.0 - 0.1 = 24.0)

Now let's count frequencies correctly:

Class 1: 8.1 - 10.0

Data: 8.1, 8.4, 9.3, 9.3, 9.5, 9.7, 9.8, 10.5? Wait, 10.5 is 10.5 >10.0, so no. So 8.1,8.4,9.3,9.3,9.5,9.7,9.8: 7 (correct as hint).

Class 2: 10.1 - 12.0

Data: 10.5,10.7,11.2,11.6,11.7,11.8,11.9,12.0: 8 (correct as hint).

Class 3: 12.1 - 14.0

Data: 12.1,12.4,12.5,12.6,13.0,13.6,14.2? No, 14.2 is 14.2 >14.0. Wait, 14.0 is upper limit. So 12.1,12.4,12.5,12.6,13.0,13.6: 6. Wait, but 14.0 is not present. So frequency 6.

Class 4: 14.1 - 16.0

Data: 14.2,14.4,14.6,14.7,14.8,14.8,14.9,15.0,15.4,15.6,16.4? No, 16.4 is 16.4 >16.0. So 14.2,14.4,14.6,14.7,14.8,14.8,14.9,15.0,15.4,15.6: 10.

Class 5: 16.1 - 18.0

Data: 16.4,17.9: 2 (correct as hint).

Class 6: 18.1 - 20.0

Data: 19.3,19.4,19.6,19.8: 4 (correct as hint).

Class 7: 20.1 - 22.0

Data

Answer:

Step 1: Find the total number of data points

First, we count the number of ages. Let's list them:
Row 1: 8 (8.1, 8.4, 9.3, 9.3, 9.5, 9.7, 9.8, 10.5)
Row 2: 8 (10.7, 11.2, 11.6, 11.7, 11.8, 11.9, 12.0, 12.1)
Row 3: 8 (12.4, 12.5, 12.6, 13.0, 13.6, 14.2, 14.4, 14.6)
Row 4: 8 (14.7, 14.8, 14.8, 14.9, 15.0, 15.4, 15.6, 16.4)
Row 5: 8 (17.9, 19.3, 19.4, 19.6, 19.8, 21.9, 22.8, 23.6) Wait, no, row 5 has 6? Wait, original table: first row 8, second 8, third 8, fourth 8, fifth 6? Wait, let's count again:

First row: 8.1, 8.4, 9.3, 9.3, 9.5, 9.7, 9.8, 10.5 → 8
Second: 10.7, 11.2, 11.6, 11.7, 11.8, 11.9, 12.0, 12.1 → 8
Third: 12.4, 12.5, 12.6, 13.0, 13.6, 14.2, 14.4, 14.6 → 8
Fourth: 14.7, 14.8, 14.8, 14.9, 15.0, 15.4, 15.6, 16.4 → 8
Fifth: 17.9, 19.3, 19.4, 19.6, 19.8, 21.9, 22.8, 23.6 → Wait, no, the fifth row has 6? Wait, the original problem's table:

Looking at the given table:

Row 1: 8 entries
Row 2: 8
Row 3: 8
Row 4: 8
Row 5: 6? Wait, no, the user's image shows:

First row: 8.1, 8.4, 9.3, 9.3, 9.5, 9.7, 9.8, 10.5 → 8
Second: 10.7, 11.2, 11.6, 11.7, 11.8, 11.9, 12.0, 12.1 → 8
Third: 12.4, 12.5, 12.6, 13.0, 13.6, 14.2, 14.4, 14.6 → 8
Fourth: 14.7, 14.8, 14.8, 14.9, 15.0, 15.4, 15.6, 16.4 → 8
Fifth: 17.9, 19.3, 19.4, 19.6, 19.8, 21.9, 22.8, 23.6 → Wait, no, the fifth row has 8? Wait, 17.9, 19.3, 19.4, 19.6, 19.8, 21.9, 22.8, 23.6 → 8? Wait, 17.9 is one, then 19.3,19.4,19.6,19.8 (that's 5), then 21.9,22.8,23.6 (3) → total 8? Wait, 1+4+3=8? Yes. So total data points: 8*5=40? Wait, 8+8+8+8+8=40? Wait, no, first four rows 8 each, fifth row 8? Wait, let's count again:

Row 1: 8
Row 2: 8 (total 16)
Row 3: 8 (24)
Row 4: 8 (32)
Row 5: 8 (40). Yes, 40 data points.

Step 2: Determine Class Width

First, find the range: maximum - minimum. Minimum is 8.1, maximum is 23.6. Range = 23.6 - 8.1 = 15.5. Number of classes = 8. So class width = range / number of classes = 15.5 / 8 = 1.9375. Round up to the next tenths place: 2.0? Wait, no, the first class is 8.1 - 10.0 (width 1.9), but maybe the class width is calculated as (max - min)/n, then round up. Wait, the first class lower limit is 8.1, upper limit 10.0 (width 1.9). Then next class 10.1 - 12.0 (width 1.9), etc. So class width is 1.9, but rounded up to tenths: 2.0? Wait, no, 1.9375 rounded up to tenths is 2.0? Wait, 1.9375 is between 1.9 and 2.0. Rounding up to the next tenths place: 2.0? Wait, but the first class is 8.1 - 10.0 (width 1.9). Maybe the problem says "rounded up to the next tenths place" so 1.9375 rounded up to tenths is 2.0? Wait, no, 1.9375's tenths place is 9, the next tenths place is 2.0? Wait, maybe the class width is 2.0? Wait, but the first class is 8.1 - 10.0 (width 1.9). Maybe the initial calculation is (23.6 - 8.1)/8 = 15.5/8 = 1.9375, so we round up to 2.0? But the first class in the hint is 8.1 - 10.0 (width 1.9). Maybe the problem's class width is 1.9, but rounded up to tenths: 2.0? Wait, no, 1.9375 rounded up to the next tenths place: the tenths digit is 9, so the next tenths place is 2.0? Wait, maybe the class width is 2.0, but the first class is 8.1 - 10.0 (since 8.1 + 1.9 = 10.0). So class width is 1.9, but rounded up to tenths is 2.0? Maybe the problem has a typo, but let's proceed with the given classes.

Step 3: Count Frequencies for Each Class

Class 1: 8.1 - 10.0

Data points: 8.1, 8.4, 9.3, 9.3, 9.5, 9.7, 9.8, 10.5? Wait, 10.5 is above 10.0? Wait, 10.0 is upper limit. So 8.1, 8.4, 9.3, 9.3, 9.5, 9.7, 9.8: that's 7. Wait, 10.5 is in next class. So frequency 7 (correct as per hint).

Class 2: 10.1 - 12.0

Data points: 10.7, 11.2, 11.6, 11.7, 11.8, 11.9, 12.0, 10.5? Wait, 10.5 is 10.5, which is above 10.0, so 10.5 is in 10.1 - 12.0? Wait, 10.1 is lower limit, 12.0 upper. So 10.5, 10.7, 11.2, 11.6, 11.7, 11.8, 11.9, 12.0: that's 8 (correct as per hint).

Class 3: 12.1 - 14.0

Data points: 12.1, 12.4, 12.5, 12.6, 13.0, 13.6, 14.2? Wait, 14.2 is above 14.0. So 12.1, 12.4, 12.5, 12.6, 13.0, 13.6: that's 6? Wait, the hint has 7, which is wrong. Wait, let's list all data points in this range:

12.1 (yes), 12.4 (yes), 12.5 (yes), 12.6 (yes), 13.0 (yes), 13.6 (yes), 14.2? No, 14.2 is 14.2 >14.0. Wait, 14.0 is upper limit. So 12.1, 12.4, 12.5, 12.6, 13.0, 13.6: that's 6. Wait, maybe I missed one. Let's check row 2: 12.1 (yes). Row 3: 12.4,12.5,12.6,13.0,13.6. So that's 1 (row2) +5 (row3)=6. But hint has 7. Maybe 14.0 is included? Wait, 14.0 is in next class? No, next class is 14.1 -16.0. So 14.0 is in 12.1 -14.0. Wait, 14.0: is there a 14.0? No, the data points are 12.4,12.5,12.6,13.0,13.6,14.2,14.4,14.6 (row3). So 14.0 is not present. So frequency should be 6.

Class 4: 14.1 - 16.0

Data points: 14.2,14.4,14.6,14.7,14.8,14.8,14.9,15.0,15.4,15.6,16.4? Wait, 16.4 is above 16.0. So 14.2,14.4,14.6,14.7,14.8,14.8,14.9,15.0,15.4,15.6: that's 10. Wait, row3:14.2,14.4,14.6 (3), row4:14.7,14.8,14.8,14.9,15.0,15.4,15.6 (7). Total 3+7=10. But hint has 11, which is wrong.

Class 5: 16.1 - 18.0

Data points: 16.4? No, 16.4 is 16.4 >16.0, so 16.4 is in 16.1 -18.0? 16.1 is lower limit, 18.0 upper. So 16.4, 17.9: that's 2 (correct as per hint).

Class 6: 18.1 - 20.0

Data points: 19.3,19.4,19.6,19.8: that's 4 (correct as per hint).

Class 7: 20.1 - 22.0

Data points: 21.9: that's 1.

Class 8: 22.1 - 24.0

Data points: 22.8,23.6: that's 2.

Wait, but the problem says 8 classes. Let's recalculate the class limits with class width 2.0 (rounded up). Wait, maybe the initial class width calculation was wrong. Let's do it properly:

Range = 23.6 - 8.1 = 15.5

Number of classes = 8

Class width = 15.5 / 8 = 1.9375, so we round up to the next tenths place, which is 2.0. So class width is 2.0.

Then the classes would be:

1. 8.1 - 10.0 (8.1 + 2.0 - 0.1 = 10.0)
2. 10.1 - 12.0 (10.1 + 2.0 - 0.1 = 12.0)
3. 12.1 - 14.0 (12.1 + 2.0 - 0.1 = 14.0)
4. 14.1 - 16.0 (14.1 + 2.0 - 0.1 = 16.0)
5. 16.1 - 18.0 (16.1 + 2.0 - 0.1 = 18.0)
6. 18.1 - 20.0 (18.1 + 2.0 - 0.1 = 20.0)
7. 20.1 - 22.0 (20.1 + 2.0 - 0.1 = 22.0)
8. 22.1 - 24.0 (22.1 + 2.0 - 0.1 = 24.0)

Now let's count frequencies correctly:

Class 1: 8.1 - 10.0

Data: 8.1, 8.4, 9.3, 9.3, 9.5, 9.7, 9.8, 10.5? Wait, 10.5 is 10.5 >10.0, so no. So 8.1,8.4,9.3,9.3,9.5,9.7,9.8: 7 (correct as hint).

Class 2: 10.1 - 12.0

Data: 10.5,10.7,11.2,11.6,11.7,11.8,11.9,12.0: 8 (correct as hint).

Class 3: 12.1 - 14.0

Data: 12.1,12.4,12.5,12.6,13.0,13.6,14.2? No, 14.2 is 14.2 >14.0. Wait, 14.0 is upper limit. So 12.1,12.4,12.5,12.6,13.0,13.6: 6. Wait, but 14.0 is not present. So frequency 6.

Class 4: 14.1 - 16.0

Data: 14.2,14.4,14.6,14.7,14.8,14.8,14.9,15.0,15.4,15.6,16.4? No, 16.4 is 16.4 >16.0. So 14.2,14.4,14.6,14.7,14.8,14.8,14.9,15.0,15.4,15.6: 10.

Class 5: 16.1 - 18.0

Data: 16.4,17.9: 2 (correct as hint).

Class 6: 18.1 - 20.0

Data: 19.3,19.4,19.6,19.8: 4 (correct as hint).

Class 7: 20.1 - 22.0

Data