Question

practice: measures of central tendency
example 1: find the mean, median, mode, and range of the following data.
$350, $150, $100, $350, $50
mean:
median:
mode:
range:
example 2: find the mean, median, mode, and range of the following data.
92%, 100%, 80%, 88%, 70%, 80%
mean:
median:
mode:
range:

Explanation:

Example 1: Data set: $\$50, \$100, \$150, \$350, \$350$ (sorted first)

Step1: Calculate mean (average)

Sum values, divide by count:
$\text{Mean} = \frac{50 + 100 + 150 + 350 + 350}{5} = \frac{1000}{5}$

Step2: Find median (middle value)

Middle term of sorted 5-value set:
$\text{Median} = 150$

Step3: Identify mode (most frequent)

Value appearing twice:
$\text{Mode} = 350$

Step4: Compute range (max-min)

Subtract min from max:
$\text{Range} = 350 - 50$

Example 2: Data set: $70\%, 80\%, 80\%, 88\%, 92\%, 100\%$ (sorted first)

Step1: Calculate mean (average)

Sum values, divide by count:
$\text{Mean} = \frac{70 + 80 + 80 + 88 + 92 + 100}{6} = \frac{510}{6}$

Step2: Find median (average of 2 middles)

Average 3rd and 4th sorted terms:
$\text{Median} = \frac{80 + 88}{2}$

Step3: Identify mode (most frequent)

Value appearing twice:
$\text{Mode} = 80\%$

Step4: Compute range (max-min)

Subtract min from max:
$\text{Range} = 100 - 70$

Answer:

Example 1:

Mean: $\$200$
Median: $\$150$
Mode: $\$350$
Range: $\$300$

Example 2:

Mean: $85\%$
Median: $84\%$
Mode: $80\%$
Range: $30\%$