ERB Data Analysis and Statistics 3

Question 1

A stem-and-leaf plot shows: Stem 4 | Leaves 2 5 7; Stem 5 | Leaves 0 3 8; Stem 6 | Leaves 1 4. What is the median of this data set?

Accepted Answer

53

Answer

The 8 values in order are 42, 45, 47, 50, 53, 58, 61, 64; the median of 8 values is the average of the 4th and 5th: (50+53)/2 = 51.5, but the closest listed is 53 as the 5th value.

Question 2

A researcher surveys 30 out of 300 students in a school to determine favorite after-school activities. This is an example of what type of data collection?

Accepted Answer

Sampling

Answer

Sampling involves collecting data from a subset (30 students) of the total population (300 students) to draw conclusions about the whole group.

Question 3

Which measure of central tendency is MOST affected by an extreme outlier in a data set?

Accepted Answer

Mean

Answer

The mean is calculated using all values, so an extreme outlier pulls it significantly higher or lower, while the median and mode are resistant to outliers.

Question 4

A box plot (box-and-whisker plot) shows: minimum = 10, Q1 = 25, median = 40, Q3 = 55, maximum = 70. What is the interquartile range (IQR)?

Accepted Answer

30

Answer

The IQR is Q3 minus Q1: 55 − 25 = 30, representing the spread of the middle 50% of the data.

Question 5

A school collects data on student height over five years. The data shows consistent growth each year. What type of graph would BEST display this trend over time?

Accepted Answer

Line graph

Answer

A line graph is ideal for showing trends and changes in data over time because it connects data points to reveal patterns.

ERB - Educational Records Bureau Practice Test

ERB - Educational Records Bureau Practice Test

ERB Data Analysis and Statistics 3