Question 16

Explanation

Initial Data Analysis

Given:

• Initial number of participants: $n_1 = 22$
• Initial average: $\bar{x}_1 = 5$
• Range: $R = 4$

Let the scores be sorted from smallest to largest as $x_1, x_2, \dots, x_{22}$.

The sum of all initial scores is:

The range is defined as the difference between the largest and smallest values:

Analysis After Removal

If the lowest score ($x_1$) and the highest score ($x_{22}$) are excluded:

• New number of participants: $n_2 = 22 - 2 = 20$
• New average: $\bar{x}_2 = 4.9$

The sum of the remaining scores is:

Calculating the Lowest Score

The relationship between the initial sum and the remaining sum is:

Substitute equation $(2)$ into equation $(3)$:

So, the lowest student's score is $4$.