Statistical Analysis

Explain the difference between mean, median, and mode in terms of central tendency.

• Mean is the most frequent value, median is the average, and mode is the middle value.

• Mean is the highest value, median is the lowest value, and mode is the average value.

• Mean is the middle value, median is the most frequent value, and mode is the lowest value.

• Mean is the average, median is the middle value, and mode is the most frequent value.

Answer explanation

Mean is the average, median is the middle value, and mode is the most frequent value.

If a data set has a mean of 20, median of 18, and mode of 22, what can you infer about the data distribution?

• Skewed to the right

• Symmetric

• Bimodal

• Skewed to the left

Answer explanation

The data distribution is skewed to the right because the mean is greater than the median and mode, indicating a tail on the right side of the distribution.

Identify any outliers in the data set: 10, 12, 14, 16, 100

• 20

• 18

• 15

• 100

Answer explanation

The outlier in the data set is 100 because it is significantly larger than the other values, making it an anomaly in the dataset.

Compare the measures of central tendency (mean, median, mode) for the data set: 2, 4, 6, 8, 10

• Mean = 5, Median = 6, Mode = No mode

• Mean = 6, Median = 6, Mode = No mode

• Mean = 7, Median = 6, Mode = No mode

• Mean = 6, Median = 5, Mode = No mode

Answer explanation

The correct measures of central tendency for the data set are: Mean = 6, Median = 6, Mode = No mode. The mean is calculated by adding all numbers and dividing by the count, the median is the middle value, and there is no mode as all values are unique.

Examine the impact of outliers on the standard deviation of a data set.

• Outliers have no impact on the standard deviation of a data set.

• Outliers decrease the standard deviation of a data set.

• Outliers can increase the standard deviation of a data set.

• Outliers always result in a standard deviation of zero.

Answer explanation

Outliers can increase the standard deviation of a data set.

Determine the mean, median, and mode for the data set: 12, 12, 14, 16, 18

• Mean = 14.4, Median = 16, Mode = 12

• Mean = 13.5, Median = 14, Mode = 18

• Mean = 15.2, Median = 14, Mode = 16

• Mean = 14.4, Median = 14, Mode = 12

Answer explanation

The mean is calculated by adding all numbers and dividing by the count, giving 14.4. The median is the middle value, which is 14. The mode is the most frequent value, which is 12.

Explain how standard deviation helps in understanding the spread of data.

• Standard deviation is used to calculate the median of a dataset

• Standard deviation helps in understanding the spread of data by quantifying the amount of variation or dispersion from the average.

• Standard deviation indicates the highest value in a dataset

• Standard deviation measures the central tendency of data

Answer explanation

Standard deviation helps in understanding the spread of data by quantifying the amount of variation or dispersion from the average.

Identify the measure of central tendency that is most affected by outliers.

• Range

• Mode

• Median

• Mean

Answer explanation

Identify the measure of central tendency that is most affected by outliers is the Mean.

Interpret the standard deviation value in relation to the mean of a data set.

• The standard deviation value indicates how much variation or dispersion exists from the mean in a data set.

• Standard deviation measures the total sum of the data set

• The standard deviation value represents the most common value in the data set

• Standard deviation is the same as the mean value in a data set

Answer explanation

The standard deviation value indicates how much variation or dispersion exists from the mean in a data set.

Discuss the scenario where mean, median, and mode are all equal in a data set.

• If mean, median, and mode are all equal in a data set, it suggests an outlier in the data.

• When mean, median, and mode are all equal in a data set, it indicates a bimodal distribution.

• The scenario where mean, median, and mode are all equal in a data set implies a skewed distribution.

• The scenario where mean, median, and mode are all equal in a data set indicates a symmetric distribution.

Answer explanation

The scenario where mean, median, and mode are all equal in a data set indicates a symmetric distribution.