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The following data represents the pounds of food collected:

```
\begin{array}{l|lllll}
0 & 5 & 6 & & \\
1 & 0 & 2 & 3 & 3 & 4 \\
2 & 1 & 9 & & \\
3 & & & & \\
4 & 2 & & & \\
5 & 1 & & & &
\end{array}
```

Calculate the following statistical measures:

- Interquartile range
- Median
- Mean
- Range

Sagot :

GinnyAnsweridn
Sure! Let's go through each of the statistical measures step-by-step: median, mean, range, and interquartile range (IQR).

1. Median:

The median is the middle value of an ordered dataset.
- First, list the data in ascending order: [0, 0, 1, 1, 2, 2, 3, 3, 4, 5, 6, 9]
- Since there are 12 data points, the median is the average of the 6th and 7th values: (2 + 3) / 2 = 2.5

2. Mean:

The mean is the average of all data points.
- Sum all the data points: 0 + 5 + 6 + 0 + 2 + 3 + 3 + 4 + 1 + 9 + 2 + 1 = 36
- Divide by the number of data points: 36 / 12 = 3.0

3. Range:

The range is the difference between the maximum and minimum values.
- Maximum value: 9
- Minimum value: 0
- Range: 9 - 0 = 9

4. Interquartile Range (IQR):

The IQR is the difference between the first quartile (Q1) and the third quartile (Q3).
- Q1 is the 25th percentile. It is the value at 1/4th of the ordered dataset.
- Q3 is the 75th percentile. It is the value at 3/4th of the ordered dataset.
- For the dataset [0, 0, 1, 1, 2, 2, 3, 3, 4, 5, 6, 9]:
- Q1 (25th percentile): The average of the 3rd and 4th values: (1 + 1) / 2 = 1
- Q3 (75th percentile): The average of the 9th and 10th values: (4 + 5) / 2 = 4.5
- IQR: Q3 - Q1 = 4.5 - 1 = 3.25

So, our final results are:
- Median: 2.5
- Mean: 3.0
- Range: 9
- IQR: 3.25

These calculations help us understand the central tendency, spread, and dispersion of the given dataset.
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