Home / Digital SAT Math Practice Questions – Medium : One-variable data: distributions and measures of center and spread

Digital SAT Math Practice Questions – Medium : One-variable data: distributions and measures of center and spread

Digital SAT Math Practice Questions - Medium : One-variable data: distributions and measures of center and spread - New Syllabus

DSAT MAth Practice questions – all topics

  • Problem-solving and Data Analysis Weightage: 15%  Questions: 5-7
    • Ratios, rates, proportional relationships, and units
    • Percentages
    • One-variable data: distributions and measures of centre and spread
    • Two-variable data: models and scatterplots
    • Probability and conditional probability
    • Inference from sample statistics and margin of error
    • Evaluating statistical claims: observational studies and Experiments

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Question Medium

The dot plot represents a data set.

Dot plot

What is the median of the 19 values in the data set?

▶️ Answer/Explanation
Solution

Answer: 42

With 19 values, median is 10th value when ordered.

Counting dots: 10th value falls at 42.

Question Medium

Data set P: 12, 18, 19, 19, 19, 19, 19, 21, 21, 22, 22

Data set \(P\) contains the lengths, in inches, of 11 objects. The length 12 inches is removed from data set \(\mathrm{P}\) to create data set \(\mathrm{N}\), which contains the lengths, in inches, of 10 objects. Which statement best compares the mean \(q\) and the median \(r\) of data set \(\mathrm{P}\) with the mean \(s\) and the median \(t\) of data set \(\mathrm{N}\)?

A) \(q < s ; r > t\)

B) \(q = s ; r > t\)

C) \(q < s ; r = t\)

D) \(q = s ; r = t\)

▶️ Answer/Explanation
Solution

Answer: C

Removing 12 increases the mean from \(q \approx 19.18\) to \(s \approx 19.9\), so \(q < s\). The median stays 19 for both \(r\) and \(t\) since the middle values remain unchanged, so \(r = t\).

Question Medium

The tables show the frequencies of data values for two data sets.

Data Set PData Set Q
ValueFrequencyValueFrequency
0141
1151
2262
3373
4686
5595
64104
73113
83123
92132

Which statement best compares the mean \(a\) and standard deviation \(b\) of data set \(\mathrm{P}\) with the mean \(c\) and standard deviation \(d\) of data set \(\mathrm{Q}\)?

A) \(a < c ; b < d\)

B) \(a < c ; b = d\)

C) \(a > c ; b = d\)

D) \(a > c ; b > d\)

▶️ Answer/Explanation
Solution

Answer: B

The mean \(c\) of Q is higher than \(a\) of P because Q’s values are shifted upward. The standard deviations \(b\) and \(d\) are similar since both sets have comparable spreads relative to their means.

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