Displaying and Summarizing Data (Dot Plots, Histograms, Box Plots) — 6th Math: Statistics & Probability practice questions

A survey of 30 students collects their height. To describe this data, you should include:

1. Just the tallest
2. Just ages
3. Just gender
4. The number of students (30), what's measured (height), the unit (inches or cm), a measure of center, and a measure of spread

Answer: D — The number of students (30), what's measured (height), the unit (inches or cm), a measure of center, and a measure of spread

Full summarization. (A), (C), (B) misread.

For 8th-grade test scores in math, which set of summary statistics is MOST INFORMATIVE?

1. Mean only
2. Sample size (n), mean OR median, range or IQR, and a brief description of shape (skewed? symmetric?)
3. Maximum only
4. The lowest score

Answer: B — Sample size (n), mean OR median, range or IQR, and a brief description of shape (skewed? symmetric?)

Multi-element summary. (A), (C), (D) understate.

Which display is best for comparing the spread and centers of two or more numerical data sets side by side?

1. Pie chart
2. Bar graph
3. Scatter plot
4. Side-by-side box plots

Answer: D — Side-by-side box plots

D) Box plots line up for direct comparison of medians, IQRs, and spreads. A) Pie charts cannot show spread. B) Bar graphs compare categories. C) Scatter plots are for two variables, not two groups.

In a class survey: 'How many hours did you sleep last night?' the data are:

1. Categorical
2. Not data
3. Random
4. Numerical — the answers are quantities, so measures like mean, median, range apply

Answer: D — Numerical — the answers are quantities, so measures like mean, median, range apply

Quantities = numerical data. (A) would be 'favorite color'; (C), (B) misread.

The five-number summary consists of:

1. Mean, median, mode, max, min
2. Mean, median, range, sum, count
3. Minimum, Q1, median, Q3, maximum
4. Q1, Q2, Q3, mean, mode

Answer: C — Minimum, Q1, median, Q3, maximum

C) Standard definition. A) Mixes center measures with extremes. B) Adds sum/count instead of quartiles. D) Includes mean and mode that don't belong.

A box plot visually displays:

1. Mean only
2. Mode only
3. The five-number summary
4. Standard deviation only

Answer: C — The five-number summary

C) Min, Q1, median, Q3, max — plus outliers as separate points. A/B/D) Single statistics, not the whole summary.

Which of these is the BEST display to identify outliers?

1. Box plot — outliers typically appear as points beyond the whiskers
2. Pie chart
3. Bar graph
4. Line graph

Answer: A — Box plot — outliers typically appear as points beyond the whiskers

A) Standard convention. B) Pie charts hide individual values. C) Bar graphs are for categories. D) Line graphs show trends, not outliers.

A histogram with bars of equal height across all intervals indicates:

1. Bimodal
2. Outliers
3. Skewed left
4. Roughly uniform distribution

Answer: D — Roughly uniform distribution

Equal heights = uniform. (A), (C), (B) misread.

In a box plot, the box itself spans from:

1. Minimum to maximum
2. Q1 to median
3. Median to Q3
4. Q1 to Q3

Answer: D — Q1 to Q3

D) The box covers the middle 50% — Q1 to Q3. A) That includes the whiskers, not just the box. B/C) Each covers only one half of the box.

To see whether data are skewed left, right, or symmetric, the BEST display is:

1. A pie chart
2. Just the mean
3. A table only
4. A histogram or dot plot — shape of the distribution is directly visible

Answer: D — A histogram or dot plot — shape of the distribution is directly visible

Shape visualization. (A), (C), (B) don't show shape.

Best plot for showing the distribution of one numerical variable?

Dot plot, histogram, or box plot.