For interval/ratio data with roughly symmetric distribution, which measures are appropriate?

For interval/ratio data with roughly symmetric distribution, which measures are appropriate?

• A. Mode and range
• B. Median and IQR
• C. Frequencies and percentages
• D. Mean and standard deviation

Answer: (D)

When data are interval or ratio and the distribution is roughly symmetric, the arithmetic mean serves as the natural measure of center because every value contributes equally to the average, and the standard deviation describes how far values typically lie from that center by averaging squared deviations. This combination uses all data points and aligns well with symmetry, giving a precise summary of both location and spread. The median and IQR are more robust to outliers and skewness, so they’re preferred when the distribution isn’t symmetric. Modes and ranges offer limited detail for continuous data, and frequencies/percentages apply to categorical data rather than summarizing a numeric distribution.

When data are interval or ratio and the distribution is roughly symmetric, the arithmetic mean serves as the natural measure of center because every value contributes equally to the average, and the standard deviation describes how far values typically lie from that center by averaging squared deviations. This combination uses all data points and aligns well with symmetry, giving a precise summary of both location and spread. The median and IQR are more robust to outliers and skewness, so they’re preferred when the distribution isn’t symmetric. Modes and ranges offer limited detail for continuous data, and frequencies/percentages apply to categorical data rather than summarizing a numeric distribution.