Question

The examination scores for 5 students are 43, 76, 64, 49, and 58. The mean, median and range for this set of data are respectively

• A. 58, 58 and 33
• B. 60, 58 and 32
• C. 64, 49 and 32
• D. 58, 49 and 33

Hint:

Statistical Calculation Sequence: 1. Always arrange the dataset in ascending order first. This gives you the minimum and maximum values for the range and reveals the median immediately. 2. Sum the values carefully to find the mean. - Arranged array: 43, 49, 58, 64, 76. (Middle value is 58; Range = 76 - 43 = 33).

Answer 1

The Correct Option is A

Concept: Evaluating a finite numerical dataset requires calculating standard descriptive statistical measures:
• Mean (\(\mu\)): The numerical average, found by dividing the sum of all observations by the number of observations.
• Median: The middle value of the dataset after arranging the numbers in ascending or descending order.
• Range: The absolute difference between the maximum and minimum values in the dataset.

Step 1: Calculating the Mean (\(\mu\)).
The dataset consists of \(n = 5\) observations: \(\{43, 76, 64, 49, 58\}\). Summing these numbers step-by-step: \[ \sum X = 43 + 76 + 64 + 49 + 58 \] \[ 43 + 76 = 119 \] \[ 119 + 64 = 183 \] \[ 183 + 49 = 232 \] \[ 232 + 58 = 290 \] Now, divide the total sum by the number of students (\(n = 5\)): \[ \mu = \frac{290}{5} = 58 \]

Step 2: Calculating the Median.
To find the median, the raw data must first be arranged in ascending order: \[ 43, \, 49, \, 58, \, 64, \, 76 \] Since the number of observations is odd (\(n = 5\)), the median corresponds to the exact middle position, given by the formula: \[ \text{Median position} = \frac{n + 1}{2} = \frac{5 + 1}{2} = 3^{\text{rd}} \text{ observation} \] Looking at our ordered array, the $3^{\text{rd}}$ value is 58.

Step 3: Calculating the Range.
Identify the maximum and minimum values from the ordered dataset: \[ X_{\text{max}} = 76 \] \[ X_{\text{min}} = 43 \] The mathematical formula for the range is: \[ \text{Range} = X_{\text{max}} - X_{\text{min}} = 76 - 43 = 33 \]

Step 4: Compiling the results.
Combining our calculations: Mean = 58, Median = 58, Range = 33. This sequence corresponds exactly to Option (A).