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The amount that two groups of students spent on snacks in one day is shown in the dot plots below.

Group A
A dot plot titled Group A. A number line going from 0 to 5 labeled Amount in Dollars. There are 0 dots above 0, 5 above 1, 4 above 2, 1 above 3, and 0 above 4 and 5.

Group B
A dot plot titled Group B. A number line going from 0 to 5 labeled Amount in Dollars. There is 1 dot above 0, 3 above 1, 3 above 2, 4 above 3, 1 above 4, and 3 above 5.

When looking at the differences in the statistical measurements of Group A and Group B, which differences have a value of $1 or less?
the median and the mode
the mean and the range
the mean and the median
the mode and the rangeThe amount that two groups of students spent on snacks in one day is shown in the dot plots below.

Group A
A dot plot titled Group A. A number line going from 0 to 5 labeled Amount in Dollars. There are 0 dots above 0, 5 above 1, 4 above 2, 1 above 3, and 0 above 4 and 5.

Group B
A dot plot titled Group B. A number line going from 0 to 5 labeled Amount in Dollars. There is 1 dot above 0, 3 above 1, 3 above 2, 4 above 3, 1 above 4, and 3 above 5.

When looking at the differences in the statistical measurements of Group A and Group B, which differences have a value of $1 or less?
the median and the mode
the mean and the range
the mean and the median
the mode and the range

1 answer

To determine which statistical measurements have differences of $1 or less, we first need to calculate the median, mode, mean, and range for both Group A and Group B based on the dot plot data provided.

Group A:

Values: 1 (5 times), 2 (4 times), 3 (1 time)

  • Data set: 1, 1, 1, 1, 1, 2, 2, 2, 2, 3

Median: Ordering the data, we have 1, 1, 1, 1, 1, 2, 2, 2, 2, 3. The median is the average of the 5th and 6th values: (1 + 2) / 2 = 1.5.

Mode: The mode is the most frequently occurring value, which is 1.

Mean: (15 + 24 + 3*1) / 10 = (5 + 8 + 3) / 10 = 16 / 10 = 1.6

Range: Maximum - Minimum = 3 - 1 = 2.

Group B:

Values: 0 (1 time), 1 (3 times), 2 (3 times), 3 (4 times), 4 (1 time), 5 (3 times)

  • Data set: 0, 1, 1, 1, 2, 2, 3, 3, 3, 4, 5, 5, 5

Median: Ordering the data: 0, 1, 1, 1, 2, 2, 3, 3, 3, 4, 5, 5, 5. The median is the 7th value: 3.

Mode: The mode is the most frequently occurring value, which is 3.

Mean: (01 + 13 + 23 + 34 + 41 + 53) / 13 = (0 + 3 + 6 + 12 + 4 + 15) / 13 = 40 / 13 ≈ 3.08.

Range: Maximum - Minimum = 5 - 0 = 5.

Summary of Statistics:

  • Group A: Median = 1.5, Mode = 1, Mean ≈ 1.6, Range = 2
  • Group B: Median = 3, Mode = 3, Mean ≈ 3.08, Range = 5

Differences:

  1. Median difference: |1.5 - 3| = 1.5
  2. Mode difference: |1 - 3| = 2
  3. Mean difference: |1.6 - 3.08| ≈ 1.48
  4. Range difference: |2 - 5| = 3

Conclusion:

All differences are greater than $1 except for:

  • None of the measurements have differences of $1 or less.

Based on the provided options, there are no differences that have a value of $1 or less in the outlined measurements.