Question

(50 POINTS) What is the five-number summary for the data set?

340 245 322 766 88 455 160 244 483 610 527

Answer 1

B

Explanation:

first, sort the numbers out for ease of data analysis.

88, 160, 244, 245, 322, 340, 455, 483, 527, 610, 766

next, we find the median which is the 6th number here as we have 11 numbers. the median is 340.

from here, we can deduce that the correct choice would be B.

Answer 2

B) min: 88, Q1: 244, med: 340, Q3: 527, max: 766

Explanation:

The five-number summary is a statistical summary of a dataset, consisting of the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum values, providing key insights into the data's central tendency and spread.

Minimum & Maximum values

The minimum value is the lowest value in the data set. The maximum value is the highest value in the data set. Therefore:

• Minimum value = 88
• Maximum value = 766

Median (Q2)

The median is the middle value in a data set when the values are arranged in ascending (or descending) order, dividing the data into two equal halves.

To find the median (Q2) of the given data set, first arrange it in ascending order:

88, 160, 244, 245, 322, 340, 455, 483, 527, 610, 766

As there are 11 data values, the middle value is the 6th value, so:

• Median (Q2) = 340

Lower Quartile (Q1)

The lower quartile (Q1) is the median of the data points to the left of the median. Therefore:

• Q1 = 244

Upper Quartile (Q3)

The upper quartile (Q3) is the median of the data points to the right of the median. Therefore:

• Q3 = 527

Five-Number Summary

Therefore, the five-number summary for the given data set is:

• Minimum value = 88
• Lower quartile (Q1) = 244
• Median (Q2) = 340
• Upper quartile (Q3) = 527
• Maximum = 766