Math Problem Statement

Calculate the mode, median, and mean for the dataset [5, 7, 8, 9, 7, 6], and recalculate these statistics after replacing 5 with 11.

Solution

Let's analyze and solve the given problem step by step.

Question (i)

You are tasked to find:

  1. Mod: The most frequently occurring number.
  2. Median: The middle value in the ordered data set.
  3. Mean: The average of the numbers.

Given data:

5,7,8,9,7,65, 7, 8, 9, 7, 6

  1. Reorder the data: 5,6,7,7,8,95, 6, 7, 7, 8, 9

  2. Mod: The number 7 occurs most frequently (twice).

    • Mod: 77
  3. Median: For an even number of data points, the median is the average of the two middle values: Median=7+72=7\text{Median} = \frac{7 + 7}{2} = 7

  4. Mean: Sum of the numbers: 5+6+7+7+8+9=425 + 6 + 7 + 7 + 8 + 9 = 42 Divide by the number of values: Mean=426=7\text{Mean} = \frac{42}{6} = 7

  • Summary for part (i):
    • Mod: 77
    • Median: 77
    • Mean: 77

Question (ii)

Replace the score 55 with 1111, resulting in: 6,7,7,8,9,116, 7, 7, 8, 9, 11

  1. Reorder the data: 6,7,7,8,9,116, 7, 7, 8, 9, 11

  2. Mod: The number 7 still occurs most frequently (twice).

    • Mod: 77
  3. Median: The middle values are 77 and 88: Median=7+82=7.5\text{Median} = \frac{7 + 8}{2} = 7.5

  4. Mean: Sum of the numbers: 6+7+7+8+9+11=486 + 7 + 7 + 8 + 9 + 11 = 48 Divide by the number of values: Mean=486=8\text{Mean} = \frac{48}{6} = 8

  • Summary for part (ii):
    • Mod: 77
    • Median: 7.57.5
    • Mean: 88

Final Answer:

Part (i):

  • Mod: 77
  • Median: 77
  • Mean: 77

Part (ii):

  • Mod: 77
  • Median: 7.57.5
  • Mean: 88

Would you like a detailed breakdown of any specific part?

5 Related Questions:

  1. What happens to the median if the number of data points is odd instead of even?
  2. Can a data set have more than one mode? Provide examples.
  3. How is the median affected if an extreme outlier is added to the data?
  4. What is the importance of finding the mode in real-life scenarios?
  5. Why is it useful to compare mean, median, and mode when analyzing data?

Tip:

Always reorder your data when calculating the median to

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Statistics
Mean
Median
Mode

Formulas

Mean = (Sum of all data points) / (Number of data points)
Median (for even dataset) = (Middle value 1 + Middle value 2) / 2

Theorems

Properties of central tendency

Suitable Grade Level

Grades 7-9