BOX PLOTS
HISTOGRAMS
FREQUENCY DENSITY & CUMULATIVE FREQUENCY
NORMAL DISTRIBUTION & Z-SCORES
SCATTER PLOTS
100

What does the line inside a box plot represent?

Median

100

What do the bars in a histogram represent?


Frequency within intervals/classes

100

What is the formula for frequency density?


Frequency Density= Frequency/Class Width

100

What is the shape of a normal distribution?


Symmetrical bell-shaped curve

100

What is a residual?

The difference between the observed value and predicted value

(Actual - Predicted)

200

What are the 5 key values shown in a box plot?

Minimum, lower quartile, median, upper quartile, maximum

200

A histogram has the following intervals and frequencies:

Interval - Frequency

0–5    6

5–10      9

10–15     15

Which interval contains the modal class?

10–15

200

A class interval has frequency 18 and class width 6.
Find the frequency density.

3

200

In a normal distribution, approximately what percent of data lies within 1 standard deviation of the mean?


About 68%

200

What does DUFS + Context mean?

  • D - Direction: Is the relationship positive (as one increases, the other increases) or negative (as one increases, the other decreases)?
  • U - Unusual Features: Are there any outliers (points that don't fit the general pattern) or distinct clusters of data?
  • F - Form: What is the shape of the relationship? Is it linear (straight line) or non-linear (curved)?
  • S - Strength: How closely do the data points follow the form? Use descriptive words like weak, moderate, or strong.
  • All in the context of the situation!
300

If the median is closer to the lower quartile than the upper quartile, what does this suggest about the distribution?

The data is skewed right / positively skewed

300

A histogram has these class intervals:

Interval    Frequency

0–10      12

10–20     18

20–40      20

Why would this histogram need frequency density instead of just frequency?

The class widths are unequal

300

What does a cumulative frequency graph help you estimate?


Median, quartiles, and percentiles

300

A student has a z-score of +2. What does this mean?


The score is 2 standard deviations above the mean

300

A scatter plot shows a strong positive linear association between study time and test scores.
What does “strong” mean in this context?

The points lie close to a linear pattern

400

A box plot has:

  • Minimum = 4
  • Q1 = 10
  • Median = 15
  • Q3 = 22
  • Maximum = 30

Find the interquartile range.

12

400

A histogram has:

Interval         Frequency Density

0–5               4

5–15             2

Which interval contains more data values? Why?

5–15

(Area determines frequency:
0–5 → area = 20
5–15 → area = 20
They contain the same number of values.)

400

The cumulative frequency reaches 40 at a value of 25.
What does this mean?

40 data values are less than or equal to 25

400

Student A has a z-score of 1.2.
Student B has a z-score of –0.5.
Who performed better relative to their group?

Student A

400

A scatter plot shows a correlation coefficient of r=−0.92
Describe the relationship.

Strong negative linear association

500

Two classes take a test.
Class A has a smaller IQR but the same median as Class B.
What does this tell us?


Class A’s scores are less spread out / more consistent

500

A histogram has the following information:

Interval         Frequency Density

0–4              3

4–10            5

10–20          2

Which interval has the greatest frequency?


4–10

Calculations:

  • 0–4 → 3 × 4 = 12
  • 4–10 → 5 × 6 = 30
  • 10–20 → 2 × 10 = 20
500

A class interval from 20–30 has frequency density 4.
Find the frequency.

40

500

The mean test score is 70 and the standard deviation is 5.
Find the z-score for a student who scored 82.

2.4

500

A least-squares regression line predicts:

y=4.2x+15

Interpret the slope in context if x represents hours studied and y represents exam score.

For each additional hour studied, the predicted exam score increases by 4.2 points on average

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