To construct the frequency distribution, histogram, and estimate the mode, mean, and median from the given data, we can follow these steps:
a) Frequency distribution:
Create a table with class intervals and their corresponding frequencies. Each class interval will represent a range of mass values.
Class Interval Frequency
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51-55 2
56-60 4
61-65 7
66-70 9
71-75 9
76-80 7
81-85 2
b) Histogram:
Plot a bar chart where the x-axis represents the class intervals and the y-axis represents the frequencies. The height of each bar corresponds to the frequency of that class interval.
c) Mode:
The mode is the class interval with the highest frequency in the histogram. In this case, the class interval with the highest frequency is 66-70.
d) Mean:
To find the mean, choose a suitable working mean within a class interval. For example, we can choose the mid-value of each class interval. Calculate the weighted mean by multiplying each mid-value by its corresponding frequency, summing them up, and dividing by the total frequency.
e) Median:
The median is the middle value when the data is sorted in ascending order. In this case, arrange the mass values in ascending order and find the middle value.
To check the accuracy of the estimated median (part e), you could compare it to the actual median calculated from the sorted data. If the estimated median is close to the actual median, it indicates the accuracy of the estimate.
Note: To provide more accurate calculations, please provide the exact table with class intervals and frequencies, as the given table is incomplete.