Question

pounds of food collected
0 | 5 6
1 | 0 2 3 3 4
2 | 1 9
3
4 | 2
5 | 1
interquartile range
median
mean
range

Explanation:

Step1: List data values

5, 6, 10, 12, 13, 13, 14, 21, 29, 42, 51

Step2: Calculate interquartile range

Find Q1 and Q3. Q1 = 10, Q3 = 29, IQR=Q3 - Q1 = 19. It is less affected by extreme values compared to range.

Answer:

First, list out the data set: 05, 06, 10, 12, 13, 13, 14, 21, 29, 42, 51

Step1: Calculate the range

The range is the difference between the maximum and minimum values.
Maximum value = 51, Minimum value = 5
Range = 51 - 5 = 46

Step2: Calculate the median

There are n = 11 data - points. The median is the \((\frac{n + 1}{2})\)-th value.
\(\frac{11+1}{2}=6\) - th value.
The ordered data set: 5, 6, 10, 12, 13, 13, 14, 21, 29, 42, 51
Median = 13

Step3: Calculate the mean

\(\text{Mean}=\frac{5 + 6+10+12+13+13+14+21+29+42+51}{11}=\frac{216}{11}\approx19.64\)

Step4: Calculate the inter - quartile range

First, find the lower half and upper half of the data.
The lower half (n = 5) is 5, 6, 10, 12, 13. The median of the lower half (Q1) is 10.
The upper half (n = 5) is 21, 29, 42, 51. The median of the upper half (Q3) is 29.
Inter - quartile range = Q3 - Q1 = 29 - 10 = 19

The data set is 5, 6, 10, 12, 13, 13, 14, 21, 29, 42, 51.
The range is 46, the median is 13, the mean is approximately 19.64, and the inter - quartile range is 19.

If the question is asking for a single value among the options without further context, we have calculated all of them as above. If we assume we need to just calculate one of them based on common analysis needs, for example, if we want a measure of spread that is not affected by extreme values, the inter - quartile range is a good choice. But without a clear question like "calculate the [specific measure]", we have provided all calculations.

If we assume we need to choose one of the options based on a general understanding of data analysis tasks: