To find the mean, median, mode, and range for the given set of data: 155, 135, 156, 166, 154, 166, 146, we will systematically calculate each statistic.
Step 1: Calculate the Mean
The mean is the sum of all the numbers divided by the count of the numbers.
Data: 155, 135, 156, 166, 154, 166, 146
Sum of the data: [tex]\(155 + 135 + 156 + 166 + 154 + 166 + 146 = 1078\)[/tex]
Number of elements: [tex]\(7\)[/tex]
Mean (Average): [tex]\(\frac{1078}{7} \approx 154.00\)[/tex]
Step 2: Calculate the Median
The median is the middle value when the numbers are arranged in ascending order.
Data in ascending order: 135, 146, 154, 155, 156, 166, 166
Since there are 7 numbers, the median is the fourth number in this ordered list.
Median: 155
Step 3: Calculate the Mode
The mode is the number that appears most frequently in the data set.
Data: 155, 135, 156, 166, 154, 166, 146
The number 166 appears twice, which is more frequent than any other number.
Mode: 166
Step 4: Calculate the Range
The range is the difference between the highest and lowest values in the data set.
Highest value: 166
Lowest value: 135
Range: [tex]\(166 - 135 = 31\)[/tex]
Summary:
- Mean: 154
- Median: 155
- Mode: 166
- Range: 31
Thus, the correct answer is:
mean: 154, Median: 155, mode: 166, range: 31
