Answer:
Explanation:
To determine the mean and median of the distribution of masses, we first need to calculate the midpoint of each class interval. The midpoint is found by taking the average of the lower and upper limits of each interval. Then, we multiply the midpoint by the corresponding frequency and sum up the results. Finally, we divide the sum by the total frequency to find the mean.
Here is the calculation:
Class Interval | Midpoint (x) | Frequency (f) | f * x
----------------------------------------------------
30-34.9 | 32.5 | 5 | 162.5
35-39.9 | 37.5 | 9 | 337.5
40-44.9 | 42.5 | 7 | 297.5
45-49.9 | 47.5 | 6 | 285
50-54.9 | 52.5 | 4 | 210
55-59.9 | 57.5 | 4 | 230
----------------------------------------------------
Total | | 35 | 1,522.5
Mean = (Sum of (f * x)) / (Sum of f) = 1,522.5 / 35 ≈ 43.5 kg
To find the median, we need to arrange the masses in ascending order. The cumulative frequency (cf) is calculated by summing up the frequencies as we move down the list. The median is the value that falls in the middle when the cumulative frequency reaches half of the total frequency.
Arranged Masses: 30, 30, 30, 30, 30, 35, 35, 35, 35, 35, 35, 35, 35, 35, 40, 40, 40, 40, 40, 40, 40, 45, 45, 45, 45, 45, 45, 50, 50, 50, 50, 55, 55, 55, 55
Cumulative Frequency: 5, 14, 21, 27, 31, 35
Since the total frequency is 35, the median will be the value at the (35/2 = 17.5)th position. Since it falls between the 17th and 18th values, we take the average of those two values.
Median = (40 + 40) / 2 = 40 kg
Therefore, the mean of the distribution is approximately 43.5 kg, and the median is 40 kg.