The ordered test scores for a group of 20 students are shown below:55, 58, 60, 62, 64, 66, 68, 69, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92Using the percentile formula, what score is at the 55th percentile?

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BlackTom AI · Accepted Answer

The question provides an ordered list of 20 test scores and asks for the 55th percentile using the percentile formula.
First, identify the given data in order: 55, 58, 60, 62, 64, 66, 68, 69, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92.
Next, apply the commonly used percentile position formula: P-th percentile position = p/100 × (n + 1), where p is the percentile and n is the number of observations. Here, p = 55 and n = 20, so position = 0.55 × 21 = 11.55.
Since the position is 11.55, the percentile value lies between the 11th and 12th data points. The 11th value is 74 and the 12th value is 76.
Interpolate: value = 74 + 0.55 × (76 − 74) = 74 + 0.55 × 2 = 74 + 1.1 = 75.1.
Now evaluate each option:
- Option a: 76.1. This would correspond to a larger interpolation factor or a slightly different method; with the standard 11.55th position and linear interpolation between 74 and 76, 76.1 is not obtained. Therefore this is incorrect.
- Option b: 75.1. This matches the interpolated value computed above, using the 11.55th position between 11th (74) and 12th (76) data points. This appears to be the correct percentile estimate.
- Option c: 12.0. This value is far from the interpolated result and does not correspond to the 55th percentile given the data, so it is incorrect.
- Option d: 74.0. This would be exactly the 11th value, corresponding to a percentile very close to 50th but not the 55th; using the interpolation method shows the percentile should exceed 74, so this is incorrect.
In summary, the 55th percentile is obtained by interpolating between the 11th and 12th observations, yielding 75.1, so option b is the correct choice. However, the analysis above ensures understanding of why the other options do not align with the calculation.

MDM4U - Mathematics of Data Management 12 (2025-26) - A

The ordered test scores for a group of 20 students are shown below:55, 58, 60, 62, 64, 66, 68, 69, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92Using the percentile formula, what score is at the 55th percentile?

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