Statistics 1

Measures of central tendency

Quiz Type

Practice

Subject

Mathematics

Level

Level 100

Questions

10 questions

Created By

Dekaglo Gifty

Quick Rules

Time limit: 10 minutes
Multiple attempts are not allowed
All questions must be answered to submit

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Question 1 of 10

Question 1

Basic multiple choice Remembering

What is the mean in statistics?

The average of a set of numbers

Correct

The most frequently occurring number

The middle value in a data set

The largest number in a data set

Explanation

The mean is calculated by adding all numbers together and dividing by the count of numbers, which defines it as the average.

Question 2

Basic multiple choice Remembering

Which measure of central tendency is defined as the value that appears most frequently in a data set?

Mode

Correct

Mean

Median

Range

Explanation

The mode is the value that occurs most frequently in a data set, distinguishing it from mean and median.

Question 3

Basic multiple choice Understanding

When is the median the most appropriate measure of central tendency to use?

When the data set has outliers

Correct

When all values are the same

When data is in a counting scale

When data represents a large population

Explanation

The median, being the middle value, is less affected by outliers compared to the mean, making it more appropriate in these cases.

Question 4

Basic multiple choice Understanding

What is the primary purpose of using measures of central tendency?

To summarize data and identify the center

Correct

To analyze the variability of data

To show trends over time

To predict future values

Explanation

Measures of central tendency help to summarize a set of data by finding the center or average, rather than analyzing its spread or predicting trends.

Question 5

Basic multiple choice Understanding

In a skewed distribution, which measure of central tendency is often most affected?

Mean

Correct

Median

Mode

Range

Explanation

The mean is influenced by extreme values or outliers, which can skew the average away from the center of the majority of data.

Question 6

Complex multiple choice Understanding

A teacher has the following test scores for her students: 85, 90, 78, 92, and 88. If she uses the mean as a measure of central tendency, what will be the result, and what does it indicate about the students' performance?

The mean score is 86.6, indicating that students performed below the expected grade level.

The mean score is 86.6, which shows a balanced performance across the scores.

Correct

The mean score is 90, suggesting that the majority of students scored high.

The mean score is 88, highlighting significant variation in students' test performances.

Explanation

The correct mean score calculation is (85 + 90 + 78 + 92 + 88) / 5 = 86.6. This indicates that, on average, students performed reasonably well, reflecting a balanced performance rather than skewed by high or low outliers. Other options misinterpret the mean's implication or miscalculate the value.

Question 7

Complex multiple choice Understanding

In a recent research study, the researcher compiled the monthly sales figures of five stores: Store A $2000, Store B $2500, Store C $3000, Store D $1500, and Store E $3500. If the researcher decides to present the median as the measure of central tendency, which figure should he report, and why might this measure be preferred in this scenario?

The median is $2500, which is useful in this case because it minimizes the impact of the highest sales figure.

Correct

The median is $3000, indicating the average store has significantly higher sales than others.

The median is $2000, which skewers the average down due to lower performers.

The median is $5000, showcasing the extreme high sales that are not representative.

Explanation

The median sales figure would be $2500 after ordering the data (1500, 2000, 2500, 3000, 3500). The median is preferred here as it provides a better representation of central tendency without being skewed by the extremities (like Store E's high sales). The other options miscalculate the median or misrepresent its significance.

Question 8

Case based multiple choice Understanding

[Case Scenario] A teacher wants to understand the average performance of her class on a recent math test. The scores from her 10 students are as follows: 56, 67, 78, 85, 90, 92, 95, 67, 80, 88. To find the central tendency of these scores, she decides to calculate the mean score. What is the mean score of the class based on the given data? Question: Should the teacher proceed to use the mean as the measure of central tendency for this data set?

Yes, the mean is appropriate because it includes all scores and provides a single average value.

Correct

No, the mean is inappropriate because it can be skewed by extreme values.

Yes, but only if there are no outlier scores in the dataset.

No, she should use the median instead because it represents the middle score better.

Explanation

The mean score of the students can be calculated by summing all the scores and dividing by the number of students. The scores add up to 848, which when divided by 10 gives an average (mean) of 84.8. The teacher's consideration of mean is appropriate as it reflects the average performance, and unless there are extreme outliers observed, this value tends to represent the data fairly well.

Question 9

Case based multiple choice Understanding

[Case Scenario] A restaurant tracks the number of customers it serves each evening over a month to better understand its busiest periods. The customer counts for the month are as follows: 20, 22, 24, 20, 30, 35, 30, 25, 20, 22, 30, 50, 60, 20, 25, 30, 22, 20, 30, 30. After analyzing this data, the restaurant manager decides to calculate the mode to understand the most common number of customers served. What is the mode of the customer count for the month? Question: How should the manager interpret the mode to make business decisions about staffing?

The mode indicates the most frequent customer count, suggesting optimal staffing levels for those days.

Correct

The mode is irrelevant for staffing as it does not consider total volume.

The mode is only useful if the numbers are all equal or close together.

The mode indicates that staffing should be reduced since fewer customers are served during peak hours.

Explanation

The mode in this case is 30, which means that the restaurant frequently serves 30 customers on several occasions. This information helps the manager determine peak periods for staffing, ensuring that servers are adequately available when the most customers are present, thereby optimizing service and potentially increasing sales.

Question 10

Case based multiple choice Understanding

[Case Scenario] In a recent survey about daily exercise habits among a group of 12 participants, the data collected showed the following minutes of exercise per day: 15, 22, 33, 15, 40, 45, 50, 20, 35, 30, 25, 15. The health coach wants to summarize this data using the median to find an appropriate benchmark for how much exercise is common among the participants. Question: How would the health coach calculate the median, and what might this reveal about exercise habits in the group?

To find the median, order the data and choose the middle value; this represents the typical exercise duration.

Correct

The median is not useful because it only selects one data point; averages are needed to show trends.

To find the median, average the highest and lowest values.

Once the data is ordered, the median will always be the upper value in the dataset.

Explanation

To find the median of the exercise minutes, the health coach first lists the data in increasing order: 15, 15, 15, 20, 22, 25, 30, 33, 35, 40, 45, 50. Since there are 12 values (an even number), the median is calculated by averaging the 6th and 7th values (25 and 30), which results in a median of 27.5 minutes. This indicates that half the participants exercised less than this amount, providing insight into typical exercise habits within this group.