Ask a New Question
Menu

Question 2:

Answer:

The data is concentrated more towards the higher grade intervals, indicating students generally performed better.

Sure, let’s fill in the blanks based on the provided text:

The histogram’s data is skewed to the right because most of the data is on the right side of the graph.

Because of the shape, the mean is pulled to the right of the median, and is therefore greater than the median.

The range is 50.

Describe the distribution of the data and how you can tell. What would be the most appropriate descriptor or measure of center and why? What is the mean? (show any calculations) What is the median? (show or explain calculations)

To analyze the distribution of the data represented in the dot plot, we’ll first summarize the distribution and then calculate the mean and median.

Distribution Analysis
Shape:

The data is slightly skewed to the right, as there are a few values on the higher end (e.g., 7, 10) that act as outliers compared to the rest.
Measure of Central Tendency:

In skewed distributions, the median is often a more reliable measure of central tendency than the mean because it is not affected by outliers.
Calculations
Mean Calculation:

Count the number of data points at each position (the x-axis represents the number of siblings).

Frequency list:

0 siblings: 1
1 sibling: 2
2 siblings: 3
3 siblings: 5
4 siblings: 2
5 siblings: 2
6 siblings: 1
7 siblings: 1
10 siblings: 1
Total Sum:

Calculation:

Total Number of Data Points:

Mean:


Median Calculation:

Sort the data points:

Since there are 18 data points (an even number), the median will be the average of the 9th and 10th values.

9th value: 3

10th value: 3

Median:


Summary
Distribution: Slightly right-skewed.
Mean: Approximately 3.56
Median: 3
The median is the most appropriate measure of center due to the skewness and presence of outliers.

Set Next Answer Items
Key Concepts

1 answer

Distribution Analysis

Shape:
The distribution of the data is slightly skewed to the right, which is evident from the presence of a few higher values (outliers) such as 7 and 10 siblings, while most of the data points cluster towards the lower values.

Measure of Central Tendency:
In distributions that are skewed, the median is generally the preferred measure of central tendency over the mean. This is because the mean can be disproportionately influenced by outliers, leading to a potentially misleading representation of the data's center.

Calculations

Mean Calculation: To calculate the mean, we need to compute the total sum of all data points, and then divide this sum by the total number of data points.

  1. Frequency List:

    • 0 siblings: 1
    • 1 sibling: 2
    • 2 siblings: 3
    • 3 siblings: 5
    • 4 siblings: 2
    • 5 siblings: 2
    • 6 siblings: 1
    • 7 siblings: 1
    • 10 siblings: 1

  2. Total Sum Calculation:

    • Total Siblings = (0 * 1) + (1 * 2) + (2 * 3) + (3 * 5) + (4 * 2) + (5 * 2) + (6 * 1) + (7 * 1) + (10 * 1)
    • Total Siblings = 0 + 2 + 6 + 15 + 8 + 10 + 6 + 7 + 10 = 64

  3. Total Number of Data Points:

    • Total Data Points = 1 + 2 + 3 + 5 + 2 + 2 + 1 + 1 + 1 = 18

  4. Mean Calculation:

    • Mean = Total Sum / Total Data Points = 64 / 18 ≈ 3.56

Median Calculation: To determine the median, we first need to list all the data points in order and then find the middle value.

  1. Sorted Data Points:

    • The ordered list of siblings based on the frequency is:
      • 0, 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 5, 5, 6, 7, 10

  2. Finding the Median:

    • There are 18 data points (an even number), so the median will be the average of the 9th and 10th values in the sorted list.

    • 9th value: 3

    • 10th value: 3

    • Median = (3 + 3) / 2 = 3

Summary

  • Distribution: Slightly right-skewed.
  • Mean: Approximately 3.56
  • Median: 3

The median is the most appropriate measure of center due to the skewness and presence of outliers in the data.