Question

The data for numbers of times per week that 24 students at Diggamole High eat vegetables are shown in the frequency table.

Number of Days Frequency
1 1
2 0
3 0
4 3
5 3
6 4
7 4
8 5
9 4


Part A: Which data display would you use to represent this data? Explain your reasoning. (4 points)

Part B: What, if any, are the unusual features of these data? Check for outliers, clusters, and gaps. Justify your answer mathematically. (5 points)

Part C: What is the best measure of center for these data? Explain your reasoning. (5 points)

Answer 1

Part A: To represent this data, a histogram would be an appropriate data display. A histogram consists of bars that represent different intervals or categories of data and their corresponding frequencies. In this case, the intervals would represent the number of days, and the height of each bar would represent the frequency. A histogram allows us to visualize the distribution of the data and identify any patterns or trends.

Part B: The unusual features of these data can be checked by examining outliers, clusters, and gaps.

Outliers: There are no outliers in the given data set since all the frequencies are within a reasonable range.

Clusters: The data exhibit a cluster around the middle range of the number of days. The frequencies are highest for 6, 7, and 8 days, indicating that a significant number of students eat vegetables on those days.

Gaps: There are gaps in the data, specifically for 2 and 3 days. No students reported eating vegetables for 2 or 3 days per week.

Part C: The best measure of center for these data would be the mode. The mode represents the value(s) that occur with the highest frequency in the data set. In this case, the modes would be the number of days with the highest frequency. From the given data, the modes would be 6, 7, and 8 days, as these have the highest frequency of 4. The mode is appropriate because it identifies the most common eating pattern among the students, which is eating vegetables for 6, 7, or 8 days per week.

Answer 2

A: The best way to display this data would be a histogram because it is discrete and we want to see the distribution of the number of times per week that students eat vegetables.

B: There is one cluster in the data. The majority of students (16) eat vegetables 4 to 6 times per week.

C: The median is the best measure of center for this data as it is not affected by outliers and the data is not normally distributed. The median is 6.

Part A:

A histogram would be the most appropriate data display for this data as it is discrete data and we want to see the distribution of the number of times per week that students eat vegetables.

Part B:

There are no outliers in the data. The quartiles are Q1 = 4, Q2 = 6, and Q3 = 8. The IQR is Q3 - Q1 = 8 - 4 = 4. Any value that is more than 1.5 IQRs below Q1 or above Q3 would be considered an outlier. There are no values that meet this criteria.

There are no gaps in the data. The data is continuous from 1 to 9.

There is one cluster in the data. The majority of students (16) eat vegetables 4 to 6 times per week.

Part C:

The median is the best measure of center for this data as it is not affected by outliers and the data is not normally distributed. The median is 6.

The measures of center for the data are as follows:

| Measure of Center | Value |

| Mean | 6.22 |

| Median | 6 |

| Mode | 8 |

As you can see, the median is the only measure of center that is not affected by the outlier. Additionally, the median is a more accurate representation of the center of the data as the data is not normally distributed.