Topic 11 - Remediation

What is the mean of the following data set: 4, 8, 6, 5, 3?

• 5

• 6

• 4

• 7

Answer explanation

To find the mean, add all the numbers: 4 + 8 + 6 + 5 + 3 = 26. Then divide by the count of numbers (5): 26 / 5 = 5. Thus, the mean is 5.

Calculate the median of the data set: 12, 15, 11, 14, 13.

• 12

• 13

• 14

• 15

Answer explanation

To find the median, first sort the data set: 11, 12, 13, 14, 15. The median is the middle value, which is 13 in this case.

What is the mode of the following data set: 7, 9, 7, 10, 11, 7, 12?

• 9

• 10

• 7

• 11

Answer explanation

The mode is the number that appears most frequently in a data set. In this case, 7 appears three times, more than any other number. Therefore, the mode of the data set is 7.

Find the range of the data set: 18, 22, 19, 25, 20.

• 5

• 7

• 6

• 8

Answer explanation

To find the range, subtract the smallest value (18) from the largest value (25). So, 25 - 18 = 7. Therefore, the range of the data set is 7.

Which of the following graphs is best for showing the frequency of data?

• Line graph

• Bar graph

• Pie chart

• Histogram

Answer explanation

A histogram is best for showing the frequency of data as it displays the distribution of numerical data by grouping values into bins, making it easy to visualize how often each range of values occurs.

If a data set has an outlier, what effect does it have on the mean?

• No effect

• Increases the mean

• Decreases the mean

• It can either increase or decrease the mean

Answer explanation

An outlier can significantly affect the mean by either increasing or decreasing it, depending on whether the outlier is much larger or smaller than the other data points. Thus, the correct answer is that it can either increase or decrease the mean.

Which of the following is a statistical question?

• What is your favorite color?

• How many students are in the class?

• What is the average height of students in the class?

• What time is it?

Answer explanation

The question 'What is the average height of students in the class?' is statistical because it seeks to summarize data from a group, while the other options ask for specific, non-variable information.

Which of the following data sets has an outlier?

• 3, 4, 5, 6, 50

• 10, 12, 14, 16, 18

• 7, 8, 9, 10, 11

• 20, 21, 22, 23, 24

Answer explanation

The data set 3, 4, 5, 6, 50 contains an outlier, 50, which is significantly higher than the other values. The other options have values that are more closely grouped together.

Which of the following is NOT a measure of central tendency?

• Mean

• Median

• Mode

• Range

Answer explanation

The range is a measure of dispersion, not central tendency. The mean, median, and mode are all measures that summarize a set of data by identifying the center point, while the range indicates the spread of the data.

What is the effect of an outlier on the median of a data set?

• Little to no effect

• Increases the median

• Decreases the median

• It can either increase or decrease the median

Answer explanation

An outlier does not affect the median because the median is the middle value of a data set when arranged in order. It remains unchanged regardless of extreme values, making 'No effect' the correct choice.