Question

a cherry farmer gathered a random sample 30 cherries and weighed them. below are the weights, in gram
8.3\t9.4\t9.5\t10.0\t10.0\t10.0
10.2\t10.2\t10.3\t10.6\t10.7\t11.1
11.2\t11.4\t11.4\t11.6\t11.9\t11.9
12.0\t12.2\t12.3\t12.4\t12.5\t12.6
12.7\t12.8\t13.5\t13.9\t14.1\t14.6
construct a frequency distribution (with relative frequencies) table for this information using 5 classes.
enter relative frequencies as well, rounded to two 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.
lower class limits\tupper class limits\tfrequency\trel. freq.

Explanation:

Step1: Find min, max, class width

Min = 8.3, Max = 14.6. Range = 14.6 - 8.3 = 6.3. Class width = 6.3 / 5 = 1.26, rounded up to 1.3 (next tenths place).

Step2: Define class limits

1st class: Lower = 8.3, Upper = 8.3 + 1.3 - 0.1 = 9.5 (subtract 0.1 for upper limit to avoid overlap)
2nd class: Lower = 9.6, Upper = 9.6 + 1.3 - 0.1 = 10.8
3rd class: Lower = 10.9, Upper = 10.9 + 1.3 - 0.1 = 12.1
4th class: Lower = 12.2, Upper = 12.2 + 1.3 - 0.1 = 13.4
5th class: Lower = 13.5, Upper = 13.5 + 1.3 - 0.1 = 14.7 (covers max 14.6)

Step3: Count frequencies

• 8.3 - 9.5: Values = 8.3, 9.4, 9.5 → Frequency = 3
• 9.6 - 10.8: Values = 10.0,10.0,10.0,10.2,10.2,10.3,10.6,10.7 → Frequency = 8
• 10.9 - 12.1: Values = 11.1,11.2,11.4,11.4,11.6,11.9,11.9 → Frequency = 7
• 12.2 - 13.4: Values = 12.0,12.2,12.3,12.4,12.5,12.6,12.7,12.8 → Frequency = 8
• 13.5 - 14.7: Values = 13.5,13.9,14.1,14.6 → Frequency = 4

Step4: Calculate relative frequencies

Rel. Freq = Frequency / 30

• 3/30 = 0.10
• 8/30 ≈ 0.27
• 7/30 ≈ 0.23
• 8/30 ≈ 0.27
• 4/30 ≈ 0.13

Answer:

Lower Class Limits	Upper Class Limits	Frequency	Rel. Freq.
9.6	10.8	8	0.27
10.9	12.1	7	0.23
12.2	13.4	8	0.27
13.5	14.7	4	0.13