Math Problem Statement

Adriana is a nurse who measures patients' heart rates as part of their annual checkups. The tables show the heart rates of the men and women she saw recently. Complete the sentences based on the data provided, including calculating medians and discussing the effect of removing outliers.

Solution

Let's analyze the heart rate data to complete the sentences.

1. Median Heart Rates for Men and Women

The median heart rate is the middle value when the heart rates are listed in order.

  • Men's heart rates: 62, 68, 70, 72, 75, 78, 80, 86, 110

    • Ordered list: 62, 68, 70, 72, 75, 78, 80, 86, 110
    • The median (middle value) is 75.
  • Women's heart rates: 64, 66, 68, 72, 76, 78, 80, 82

    • Ordered list: 64, 66, 68, 72, 76, 78, 80, 82
    • The median is 76.

So, the median heart rate for men is less than the median heart rate for women.

2. Effect of Removing the Outlier

The outlier in the men's heart rates is 110, which is much higher than the other values. Let's remove it and recalculate the median.

  • Men's heart rates without the outlier: 62, 68, 70, 72, 75, 78, 80, 86
    • Ordered list: 62, 68, 70, 72, 75, 78, 80, 86
    • New median = 73.5 (average of 72 and 75).

For women, there doesn't appear to be a significant outlier, so their median remains 76.

Final Results:

  • The median heart rate for the men is less than the median heart rate for the women.
  • If the outlier were removed, the median heart rate for the men would decrease and the median heart rate for the women would stay the same.

Would you like further details, or have any questions?

Related Questions:

  1. How do you calculate the mean heart rate?
  2. What would be the mode of the men's and women's heart rates?
  3. How would removing a different value (e.g., 86) affect the men's median?
  4. What is the range of heart rates for men and women?
  5. How do you interpret the impact of outliers on data?

Tip: Always organize your data when calculating statistical measures like median, mean, or range.

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Math Problem Analysis

Mathematical Concepts

Statistics
Median
Outliers

Formulas

Median = middle value of ordered data set
Outlier effect on median: removing the extreme value

Theorems

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Suitable Grade Level

Grades 6-8