Match each statistical scenario with its corresponding numerical value based on the princi… — Armed Services Vocational Aptitude Battery (ASVAB)

Match each statistical scenario with its corresponding numerical value based on the principles of central tendency.

The median of the sequence $2x-1$ , $2x+3$ , $2x$ , $2x+5$ , and $2x-4$ , given $x=6$ . $12$
The score required on a 6th assessment to raise an existing 5-assessment mean of $74$ to a new mean of $76$ . $86$
The arithmetic mean of the modes in the data set: $14, 18, 14, 22, 19, 22, 25, 21$ . $18$
The absolute difference between the mean and the median of the data set: $2, 8, 10, 15, 20$ . $1$

Cevap

The algebraic sequence median is 12, the required 6th assessment score is 86, the mean of the modes is 18, and the difference between the mean and median is 1.

Each statistical scenario is solved by accurately applying the definitions and formulas for mean, median, and mode, as detailed in the matching explanations.

Adım Adım Çözüm

Calculate the median of the algebraic sequence by substituting x=6 and sorting the results.

The substituted values are 11, 15, 12, 17, and 8. Sorted, they are 8, 11, 12, 15, 17. The median is 12.

The median requires evaluating the expressions first, then sorting the data set from least to greatest to find the positional center.

Calculate the required 6th assessment score using the mean formula.

Target sum = 6 × 76 = 456. Current sum = 5 × 74 = 370. Required score = 456 - 370 = 86.

The mean is the total sum divided by the number of values. Manipulating this formula allows isolation of the missing value.

Identify the modes of the bimodal set and average them.

The modes are 14 and 22. Their mean is (14 + 22) / 2 = 18.

The mode is the most frequent value. This set has two modes. Their average is found by adding them and dividing by 2.

Find the absolute difference between the mean and median of the final set.

Sum = 55, Mean = 55 / 5 = 11. Median = 10. Difference = |11 - 10| = 1.

Comparing multiple measures of central tendency requires calculating each independently before finding their difference.

Anahtar Kavram

Measures of Central Tendency

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Adım Adım Çözüm

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