6th Math: Statistics & Probability practice questions and exam guide

A histogram shows:

1. Frequencies in intervals (bins) for quantitative data — bars touch
2. Categories with spaces
3. Pie pieces
4. Lines

Answer: A — Frequencies in intervals (bins) for quantitative data — bars touch

A) Standard. B) Bar graph. C/D) Different.

On a box plot, if the median line is on the LEFT side of the box, the data are:

1. Symmetric
2. Skewed right (more variability in the upper half)
3. Skewed left
4. Bimodal

Answer: B — Skewed right (more variability in the upper half)

Median closer to Q1 means more spread above median → skewed right. (A), (C), (D) misread.

A student summarizes data as: 'Mean is 50, IQR is 10.' What is missing?

1. The number of observations and units
2. The maximum
3. The mode
4. A second mean

Answer: A — The number of observations and units

A) 6.SP.B.5 requires n, attribute, and units alongside center and spread. B) Max alone is not required. C) Mode is optional. D) Reporting two means is unusual.

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.

A sample with variability is shown by:

1. Values that differ from each other (spread)
2. Identical values
3. No data
4. One value

Answer: A — Values that differ from each other (spread)

A) Standard. B/C/D) Each is incorrect.

Range of 5, 8, 12, 15:

1. 5
2. 10
3. 15
4. 20

Answer: B — 10

B) Max − min = 15 − 5. A/C/D) Each is incorrect.

Add 1 outlier of 1000 to {2, 4, 6, 8}. The new mean is:

1. 5
2. 200
3. 204
4. 220

Answer: C — 204

Sum = 1020. /5 = 204. (A) is original mean; (B), (D) miscalculate.

The mean of {3, 5, 7, 9, 11} is:

1. 7
2. 5
3. 9
4. 11

Answer: A — 7

A) Sum = 35; 35 / 5 = 7. B/C) Single values, not averages. D) The maximum.

You collected ages of 20 people and reported only 'mean age = 12.' What concern does this raise?

1. The data are categorical
2. You can't tell median
3. You can't compute the range
4. Without spread/shape info, two very different age distributions could share this same mean

Answer: D — Without spread/shape info, two very different age distributions could share this same mean

D) Spread and shape are essential — 50,50,50 and 0,50,100 share a mean. A) Numerical, not categorical. B/C) Both true, but the headline issue is that summarization is incomplete.

Removing the outlier 50 from {10, 12, 12, 14, 50} changes the mean from 19.6 to:

1. 19.6
2. 14.0
3. 13.0
4. 12.0

Answer: D — 12.0

D) New sum = 10+12+12+14 = 48; 48/4 = 12.0. A) The original mean. B) Off by two. C) Off by one.

In a distribution, the "center" is most commonly measured by:

1. The mode only
2. The range
3. The mean or the median
4. The maximum value

Answer: C — The mean or the median

C) Mean and median are the standard centers. A) Mode is a center but rarely the headline. B) Range measures spread, not center. D) An extreme, not a center.

In a histogram, the vertical axis usually shows:

1. Bin width
2. Quartile location
3. The mean
4. Frequency (count) of values in each bin

Answer: D — Frequency (count) of values in each bin

D) Height = frequency. A) Bin width is on the x-axis. B) Quartiles relate to box plots. C) Mean is a number, not an axis.

Can a data set have two modes?

Yes — it's called 'bimodal' (two values tied for most common).

What is 'range'?

The difference between the largest and smallest values. Range = max − min.

Worked example — A histogram of test scores has bin heights 2, 5, 9, 6, 3 from low to high. Is it symmetric or skewed?

Step 1: List the bar heights left → right: 2, 5, 9, 6, 3. Step 2: The tallest bar is in the middle (9). Step 3: Compare the two sides. Left of peak: 2, 5. Right of peak: 6, 3. Approximately mirror — both descend. Step 4: Heights drop off similarly on both sides → symmetric (roughly mound-shaped). Answer: approximately symmetric.

What is Q3?

Median of upper half — 75th percentile.

What is Q1?

Median of lower half — 25th percentile.

What are the 'measures of center'?

Mean, median, and mode. They describe a typical or middle value.