Question

The chess club at a school has 15 members. The number of games won in tournament play this season by each member is listed.

{ 6, 6, 6, 7, 10, 11, 12, 13, 14, 14, 15, 16, 18, 18, 30 }
What measure is most appropriate for describing variability in this data distribution

Answer 1

The most appropriate measure for describing the variability in this data distribution is the range, which is calculated by subtracting the lowest value from the highest value in the data set. In this case, the range is 24.

Step-by-step explanation:

The measure most appropriate for describing the variability in this data distribution is the range. The range is calculated by subtracting the lowest value from the highest value in the data set. In this case, the lowest value is 6 and the highest value is 30, so the range is 30 - 6 = 24.

Answer 2

The most appropriate measure for describing variability in this data set, which includes a potential outlier, is the interquartile range (IQR) as it is not heavily influenced by extreme values.

Step-by-step explanation:

The question asks about determining the most appropriate measure for describing variability in a data distribution of games won by members of a chess club. Considering the provided data set {6, 6, 6, 7, 10, 11, 12, 13, 14, 14, 15, 16, 18, 18, 30}, we note that there is one particularly high value (30), which could be an outlier. Therefore, to describe the variability in this data set, a measure that is less affected by outliers, such as the interquartile range (IQR), would be more appropriate than options like variance or standard deviation. The IQR is the difference between the third quartile (Q3) and the first quartile (Q1), essentially measuring the spread of the middle 50% of the values.