Scenario: Test Score Analysis - Learn to calculate mean, median, mode, and range through academic performance analysis!
A math teacher wants to analyze the performance of her class on a recent test. The scores are: 85, 92, 78, 96, 88, 82, 90, 85, 94, 87, 89, 91, 83, 86, 93. She needs to find the mean, median, mode, and range.
Analysis Challenge:
Calculate all four measures of center and spread to understand class performance.
Raw Scores: 85, 92, 78, 96, 88, 82, 90, 85, 94, 87, 89, 91, 83, 86, 93
First, let's organize the data in order: 78, 82, 83, 85, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 96
Mean: The sum of all values divided by the number of values.
Formula: Mean = Sum of all values ÷ Number of values
Step 1: Add all the scores
85 + 92 + 78 + 96 + 88 + 82 + 90 + 85 + 94 + 87 + 89 + 91 + 83 + 86 + 93 = 1,338
Step 2: Count the number of scores
There are 15 scores
Step 3: Divide sum by count
Mean = 1,338 ÷ 15 = 89.2
Median: The middle value when data is arranged in order.
For odd number of values: middle value
For even number of values: average of two middle values
Step 1: Arrange scores in order
78, 82, 83, 85, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 96
Step 2: Find the middle position
With 15 scores, the middle is the 8th score (position 8)
Step 3: Identify the median
The 8th score is 88, so Median = 88
Mode: The value that appears most frequently in the data set.
A data set can have no mode, one mode, or multiple modes.
Looking at the ordered scores: 78, 82, 83, 85, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 96
The score 85 appears twice, all others appear once. Therefore, Mode = 85
Range: The difference between the highest and lowest values.
Formula: Range = Highest value - Lowest value
Highest score: 96
Lowest score: 78
Range = 96 - 78 = 18
Mean: 89.2 (average score)
Median: 88 (middle score)
Mode: 85 (most frequent)
Range: 18 (spread of scores)
Interpretation: The class performed well with an average of 89.2. The median of 88 shows that half the students scored 88 or higher. The range of 18 indicates moderate variation in performance.
Find the mean, median, mode, and range for: 12, 15, 18, 12, 20, 16, 14, 12, 19
Your calculations:
A student scored 95 on a test where the class mean was 78 and median was 80. How did this student perform compared to the class?
Your analysis: