Question

matching.
match the measure of center with its description.
column a column b

1. mean a. also called average is found by adding all values together and dividing by the number of items in the set.
2. median b. the value that occurs most often in a data set.
3. mode c. the middle value when all data values are listed from least to greatest.

question 5 (1 point)
matching.
match the measure of variability with its description
column a column b

1. range a. represents the middle 50% of data.
2. standard deviation b. how far a typical data value is from the mean.
3. interquartile range (iqr) c. maximum value - minimum value

Explanation:

1.

• Mean: By definition, the mean (average) is calculated as $\frac{\sum_{i = 1}^{n}x_{i}}{n}$ (sum of values divided by the number of values), which matches description a.
• Median: When data is ordered from least to greatest, the median is the middle - value. For a set with \(n\) values (\(n\) odd: \(\frac{n + 1}{2}\)th value; \(n\) even: average of \(\frac{n}{2}\)th and \((\frac{n}{2}+1)\)th values), which matches description c.
• Mode: It is the value that appears most frequently in a data - set, which matches description b.

2.

• Range: The range is simply the difference between the maximum and minimum values in a data - set (\(R=\text{Max}-\text{Min}\)), which matches description c.
• Standard Deviation: It measures the dispersion of data points around the mean. A low standard deviation indicates that data points are close to the mean, and a high standard deviation indicates that data points are spread out. In other words, it shows how far a “typical” data value is from the mean, which matches description b.
• Interquartile Range (IQR): The IQR is \(Q_{3}-Q_{1}\), where \(Q_{1}\) is the first quartile (25th percentile) and \(Q_{3}\) is the third quartile (75th percentile). So, it represents the middle 50% of the data, which matches description a.

Answer:

1. Mean - a, Median - c, Mode - b
2. Range - c, Standard Deviation - b, Interquartile Range (IQR) - a