Answer :
To solve this problem, we need to calculate four statistical measures: the range, mode, median, and mean of the masses of the six newborn elephants. Let's break each one down step-by-step.
a) Range:
The range is the difference between the highest and lowest values in a set.
- The given masses are: 102 kg, 105 kg, 93 kg, 93 kg, 100 kg, and 107 kg.
- The highest mass is 107 kg and the lowest mass is 93 kg.
- Range = Highest mass - Lowest mass = 107 kg - 93 kg = 14 kg.
b) Mode:
The mode is the number that appears most frequently in a set.
- In the list of masses (102 kg, 105 kg, 93 kg, 93 kg, 100 kg, 107 kg), the number 93 kg appears twice, while all other numbers appear only once.
- Therefore, the mode is 93 kg.
c) Median:
The median is the middle number of a set when it is ordered from least to greatest.
- First, order the masses: 93 kg, 93 kg, 100 kg, 102 kg, 105 kg, 107 kg.
- With six elephants, the median will be the average of the third and fourth numbers.
- Median = (100 kg + 102 kg) / 2 = 202 kg / 2 = 101 kg.
d) Mean:
The mean is the average of the numbers in a set.
- Add all the masses together: 102 kg + 105 kg + 93 kg + 93 kg + 100 kg + 107 kg = 600 kg.
- Divide the total by the number of masses: 600 kg ÷ 6 = 100 kg.
- The mean mass is 100 kg.
b) Best Average Description:
The median is often the best measure of central tendency when there are outliers or when the data set is small and unbalanced. In this case, the mean, 100 kg, is slightly lower than the median due to the presence of two lower values (93 kg). However, the median (101 kg) still represents the central data accurately without being skewed by the low numbers. Thus, the median provides the best average description of the masses of the newborn elephants.
