Answer :
Step-by-step explanation:
Given data: 30, 32, 19, 48, 40, 25, 19, 18, 39, 24
### a. Range
The range is calculated as the difference between the maximum and minimum values in the data set.
1. **Arrange the data in ascending order**:
18, 19, 19, 24, 25, 30, 32, 39, 40, 48
2. **Calculate the range**:
- Minimum value = 18
- Maximum value = 48
Range = Maximum value - Minimum value
Range = 48 - 18
Range = 30
So, the range of the data set is **30**.
### b. Mean (Average)
The mean is the sum of all values divided by the number of values.
1. **Sum of the data**:
Sum = 30 + 32 + 19 + 48 + 40 + 25 + 19 + 18 + 39 + 24
= 294
2. **Number of values (n)**:
n = 10
3. **Calculate the mean**:
Mean = Sum / n
= 294 / 10
= 29.4
So, the mean (average) of the data set is **29.4**.
### c. Median
The median is the middle value in a sorted, ascending or descending, list of numbers.
1. **Arrange the data in ascending order** (already done):
18, 19, 19, 24, 25, 30, 32, 39, 40, 48
2. **Identify the middle value**:
- Since there are 10 values, the median will be the average of the 5th and 6th values.
Median = (25 + 30) / 2
= 55 / 2
= 27.5
So, the median of the data set is **27.5**.
### d. Mode
The mode is the value that appears most frequently in the data set.
1. **Identify the frequency of each value**:
- 18 appears 1 time
- 19 appears 2 times
- 24 appears 1 time
- 25 appears 1 time
- 30 appears 1 time
- 32 appears 1 time
- 39 appears 1 time
- 40 appears 1 time
- 48 appears 1 time
2. **Determine the mode**:
- The value 19 appears most frequently (2 times).
Therefore, the mode of the data set is **19**.
### Summary of Results:
- Range: **30**
- Mean: **29.4**
- Median: **27.5**
- Mode: **19**
These are the statistical measures for the given data set.