Let's break down the questions presented in the image:

Data Set:

The number of people on 22 different trips: 31, 38, 41, 41, 41, 43, 46, 47, 48, 48, 48, 49, 51, 51, 51, 52, 53, 53, 54, 54, 54, 54

Frequency Distribution:

The bar chart shows the number of trips for each range of people. The exact distribution is:

• 1 trip with 30–35 people (includes 31)
• 1 trip with 35–40 people (includes 38)
• 4 trips with 40–45 people (41 appears 3 times, 43 once)
• 6 trips with 45–50 people (46, 47, 48 appears 3 times, 49)
• 10 trips with 50–55 people (51 appears 3 times, 52, 53 twice, 54 appears 4 times)

Questions:

1. (a) Which measures of central tendency (mean, median, mode) take more than one value?

   • Mode: The mode takes multiple values because there are multiple most frequent values (51, 54). Therefore, it takes more than one value.
   • Mean and Median are single values.

2. (b) If the smallest value (31) is replaced by 17, which measures of central tendency are affected?

   • Mean: Yes, because the mean depends on all the data values. Changing 31 to 17 will lower the mean.
   • Median: No, because the median depends on the middle value, and changing an extreme value like 31 does not affect the central part of the data.
   • Mode: No, because the mode is based on the most frequent values, and 31 was not the mode.

Would you like further details on any of these concepts?

Related Questions:

1. How do you calculate the mean for a data set like this?
2. What is the definition of mode and why does it allow multiple values?
3. How is the median found, and why isn’t it affected by extreme values?
4. What impact would changing other values (besides 31) have on the mean or median?
5. Can a data set ever have more than one median?

Tip:

Always remember that mean is sensitive to all data points, while median is resistant to changes in extreme values.