There are different ways to analyze a data set, depending on the goals and context of the analysis. Here are some possible steps for analyzing this data set:
1. Calculate some summary statistics:
- Mean (average): (49 + 50 + 45 + 23 + 35 + 66 + 34 + 74 + 54 + 50) / 10 = 46.6
- Median (middle value): arrange the data in order and find the value that splits the data in half (half above and half below). In this case, the data in order is: 23, 34, 35, 45, 50, 50, 54, 66, 74. The median is the average of the two middle values, which are 50 and 54. So the median is (50 + 54) / 2 = 52.
- Mode (most frequent value): there are two values that occur twice each, which are 50 and 45. So both 50 and 45 are modes.
2. Check the range (difference between the highest and lowest values): 74 - 23 = 51.
3. Check the interquartile range (IQR, difference between the third and first quartiles): to do this, we need to find the quartiles, which split the data into four equal parts. The first quartile (Q1) is the median of the lower half of the data, which is (23, 34, 35, 45, 50) = 35. The third quartile (Q3) is the median of the upper half of the data, which is (50, 54, 66, 74) = 60. So IQR = Q3 - Q1 = 60 - 35 = 25.
4. Create a box plot to visualize the distribution of the data. A box plot shows the median, quartiles, range, and outliers (values that are more than 1.5 times the IQR away from Q1 or Q3). Here's how to draw a box plot for this data set:
- draw a number line and mark the lowest and highest values: 23 and 74
- draw a vertical line through the median: 52
- draw a box from Q1 to Q3: the bottom of the box is Q1 (35), the top of the box is Q3 (60), and the median line goes through the box
- draw whiskers (lines) from the box to the lowest and highest values that are not outliers: for the lower whisker, we can use 23 since it's the lowest value; for the upper whisker, we can use 66 since it's the highest value that's not an outlier. (A value has to be more than 1.5*IQR away from Q1 or Q3 to be an outlier - in this case, that means more than 1.5*25 = 37.5 away from Q1 or Q3). There are no outliers in this case.
| | |
| |--------------| |----
| | 74
|--------------| | |
| 66 |
|-------------------| |
54
|
50 |----
|
|
45 |
|
|
35 |
|
|
23 |
5. Consider the shape of the distribution. From the summary statistics and box plot, we can see that the data set has a mean that is slightly lower than the median, indicating that there may be some skewness or outliers on the lower end. The box plot confirms this with a longer tail on the lower whisker. However, the data set is not strongly skewed or bimodal (having two distinct peaks), and the range and IQR are relatively small compared to the spread of the data. Overall, we might describe the data as moderately spread out with some outliers on the lower end, but with a generally symmetrical shape.
Consider this data set:
{49, 50, 45, 23, 35, 66, 34, 74, 54, 50}
1 answer