The table below shows the heights of 6 members of a basketball team.
player: 1 , 2 , 3 , 4 , 5 , 6
height(in.): 54 , 60 , 82 , 60 , 84 , 65
Which measure best describes the team in terms of height?
a. range
b. mode
c. median
d. mean
Median
To determine the measure that best describes the team in terms of height, we need to consider each option and calculate their values based on the given data.
a. Range: The range is the difference between the highest and lowest values. In this case, the highest value is 84 inches, and the lowest value is 54 inches. Therefore, the range is 84 - 54 = 30 inches.
b. Mode: The mode is the value that appears most frequently in the data. In this case, there is no value that appears more than once, so there is no mode.
c. Median: The median is the middle value when the data is arranged in ascending or descending order. To find the median, we need to arrange the heights in ascending order: 54, 60, 60, 65, 82, 84. Since there is an even number of values, we take the average of the two middle values: (60 + 65) / 2 = 62.5 inches.
d. Mean: The mean is calculated by summing all the values and dividing by the total number of values. Summing the heights: 54 + 60 + 82 + 60 + 84 + 65 = 405 inches. Then dividing by the total number of values (6), we get: 405 / 6 = 67.5 inches.
Based on the calculations, the measures are as follows:
a. range: 30 inches
b. mode: No mode
c. median: 62.5 inches
d. mean: 67.5 inches
Comparing these measures, the best measure that describes the team's height would depend on the specific context and the aspect of height one wants to emphasize. For example, if we are concerned with the spread of heights, the range would be a suitable measure. If we are interested in the typical height observed, the median or mean would be more appropriate.