Calculate Mode Median Mean Range Variance and Standard Deviation for Home Prices

Published on October 15, 2026

Statistics

This problem requires finding the mode, median, mean, range, sample variance, and sample standard deviation for a dataset of single family home prices. The solution involves ordering the data, identifying the most frequent value, calculating central tendency measures, and determining variability using statistical formulas.

Question

solve it all 3 and show all procedure

Answer

Here are the step-by-step solutions for each data set.

1) Single Family Home Prices

Data Set:
205300, 204600, 212200, 209100, 189300, 212200, 180000, 215800, 211900, 207800, 193500, 214700, 184400, 197400, 204000, 210900, 209300, 199600, 205400, 199400, 201000, 203900, 181300.
(

)

Step 1: Order the data from least to greatest.
180000, 181300, 184400, 189300, 193500, 197400, 199400, 199600, 201000, 203900, 204000, 204600, 205300, 205400, 207800, 209100, 209300, 210900, 211900, 212200, 212200, 214700, 215800.

Step 2: Find the Mode.
The number that appears most frequently is 212,200.
Mode = 212,200

Step 3: Find the Median.
Since

is odd, the median is the value at position

.
The 12th value in the ordered list is 204,600.
Median = 204,600

Step 4: Find the Mean ().
Sum of all values