Question

Use the images to answer the question.

Graph 1

A dot plot titled assessment score per student has a horizontal axis ranging from 72 to 94 in increments of 2.
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The data points show 4 dots above 72, 2 dots above 74, 0 dots above 76, 4 dots above 78, 0 dots above 80, 1 dot above 82, 5 dots above 84, 0 dots above 86, 3 dots above 88, 1 dot above 90, 0 dots above 92, and 3 dots above 94.


Graph 2

A dot plot titled Assessment Score per Student has a horizontal axis ranging from 76 to 98 in increments of 2.
▼Click for Long Desc
The data points show 0 dots above 76. 1 dot above 78, 5 dots above 80, 4 dots above 82, 3 dots above number 84, 2 dots above 86, 1 dot above 88, 2 dots above 90, 0 dots above 92, 4 dots above 94, 0 dots above 96, and 1 dot above 98.


Which of the two graphs has a larger average deviation?

(1 point)
Responses

The first graph has a larger average deviation.
The first graph has a larger average deviation.

The average deviation is the same for both graphs.
The average deviation is the same for both graphs.

The second graph has a larger average deviation.
The second graph has a larger average deviation.

It is impossible to tell from these datasets.
It is impossible to tell from these datasets.

Answer 1

The first graph has a larger average deviation.

Work:
- Graph 1: n = 23, mean = 1886/23 = 82.0. Sum |x − mean| = 144, so MAD = 144/23 ≈ 6.26.
- Graph 2: n = 23, mean = 1972/23 ≈ 85.74. Sum |x − mean| ≈ 113.22, so MAD ≈ 113.22/23 ≈ 4.93.

Since 6.26 > 4.93, the first graph has the larger average deviation.