Research Methods- Data analysis: Descriptive statistics

Question 1

Descriptive statistics -

Answer 1

The use of graphs, tables and summary statistics to identify trends and analyse sets of data.

Question 2

Measures of central tendency -

Answer 2

The general term for any measure of the average value in a set of data.

Question 3

Mean -

Answer 3

The arithmetic average calculated by adding up all the values in a set of data and dividing by the number of values there are.

Question 4

Median -

Answer 4

The central value in a set of data when values are arranged from lowest to highest.

Question 5

Mode -

Answer 5

The most frequently occurring value in a set of data.

Question 6

What are measures of central tendency?

Answer 6

Measures of central tendency are averages that provide information about the most typical values in a dataset. The three main measures are the mean, median, and mode.

Question 7

What is the mean?

Answer 7

The mean is the arithmetic average, calculated by adding all scores in a dataset and dividing by the total number of scores.

Question 8

How is the mean calculated?

Answer 8

For the dataset: 5, 7, 7, 9, 10, 11, 12, 14, 15, 17, the mean is calculated as (5+7+7+9+10+11+12+14+15+17) ÷ 10 = 10.7.

Question 9

What is a strength of the mean?

Answer 9

It is the most sensitive measure of central tendency as it includes all scores in the dataset, making it representative of the data as a whole.

Question 10

What is a limitation of the mean?

Answer 10

It can be easily distorted by extreme values. For example, replacing 17 with 98 changes the mean to 18.8, which is not representative of the dataset.

Question 11

What is the median?

Answer 11

The median is the middle value in a dataset when scores are arranged in order.

Question 12

How is the median calculated?

Answer 12

For an even number of scores, the median is the average of the two middle values. In the dataset: 5, 7, 7, 9, 10, 11, 12, 14, 15, 17, the median is (10 + 11) ÷ 2 = 10.5.

Question 13

What is a strength of the median?

Answer 13

It is not affected by extreme values, making it more reliable for datasets with outliers.

Question 14

What is a limitation of the median?

Answer 14

It is less sensitive than the mean because it does not include all scores in the calculation.

Question 15

What is the mode?

Answer 15

The mode is the most frequently occurring value in a dataset.

Question 16

What is an example of the mode?

Answer 16

In the dataset: 5, 7, 7, 9, 10, 11, 12, 14, 15, 17, the mode is 7.

Question 17

What is a limitation of the mode?

Answer 17

It is a crude measure and may not be representative of the dataset as a whole.

Question 17

What is a strength of the mode?

Answer 17

It is easy to calculate and is the only measure of central tendency that can be used for categorical data.

Question 18

What is a bimodal dataset?

Answer 18

A bimodal dataset has two modes, meaning two values occur with the same highest frequency.

Question 19

What are measures of dispersion?

Answer 19

Measures of dispersion describe how spread out the scores in a dataset are. The two main measures are the range and standard deviation.

Question 20

What is the range?

Answer 20

The range is the difference between the highest and lowest values in a dataset, often calculated as (highest value - lowest value) + 1.

Question 21

How is the range calculated?

Answer 21

For the dataset: 5, 7, 7, 9, 10, 11, 12, 14, 15, 17, the range is (17 - 5) + 1 = 13.

Question 22

What is a strength of the range?

Answer 22

It is easy to calculate and provides a quick measure of spread.

Question 23

What is a limitation of the range?

Answer 23

It only considers the two extreme values, which may not represent the overall spread of the dataset.

Question 24

What is standard deviation?

Answer 24

Standard deviation is a measure of how far scores deviate from the mean, providing a precise measure of dispersion.

Question 25

What does a high standard deviation indicate?

Answer 25

A high standard deviation indicates that scores are widely spread, suggesting variability in responses or effects.

Question 26

What does a low standard deviation indicate?

Answer 26

A low standard deviation indicates that scores are tightly clustered around the mean, suggesting consistency in responses or effects.

Question 27

What is a strength of standard deviation?

Answer 27

It includes all values in the calculation, providing a precise measure of dispersion.

Question 28

What is a limitation of standard deviation?

Answer 28

It can be distorted by extreme values, similar to the mean.

Question 29

What is an example of a dataset with a misleading range?

Answer 29

In the dataset: 0, 47, 49, 50, 50, 50, 51, 53, 54, 56, 56, 57, 100, the range is 101, but most scores are clustered around 50, making the range unrepresentative.

Question 30

What is the purpose of adding 1 to the range?

Answer 30

Adding 1 accounts for rounding errors in raw scores, ensuring the range accurately reflects the spread of data.

Question 31

What is the relationship between standard deviation and the mean?

Answer 31

Standard deviation measures how far scores deviate from the mean, providing insight into the variability of the dataset.

Question 32

What is an example of a dataset with a low standard deviation?

Answer 32

A dataset with scores: 10, 11, 12, 11, 10 has a low standard deviation, indicating scores are close to the mean.

Question 33

What is an example of a dataset with a high standard deviation?

Answer 33

A dataset with scores: 5, 20, 35, 50, 65 has a high standard deviation, indicating scores are widely spread.

Question 34

What is the importance of measures of central tendency?

Answer 34

They provide a summary of the most typical or central values in a dataset, helping researchers understand the overall pattern of data.

Question 35

What is the importance of measures of dispersion?

Answer 35

They describe the spread or variability of scores, providing insight into the consistency or variability of responses in a dataset.

Question 36

What is the difference between the mean and the median?

Answer 36

The mean is the arithmetic average, while the median is the middle value. The mean is sensitive to extreme values, whereas the median is not.

Question 37

What is the difference between the range and standard deviation?

Answer 37

The range is a simple measure of spread based on extreme values, while standard deviation is a precise measure of how far scores deviate from the mean.

Question 38

What is the role of the mode in categorical data?

Answer 38

The mode is the only measure of central tendency that can be used for categorical data, identifying the most frequently occurring category.

Question 39

What is an example of a dataset with no mode?

Answer 39

A dataset with scores: 5, 7, 9, 11, 13 has no mode, as all values occur with the same frequency.

Question 40

What is the significance of standard deviation in experiments?

Answer 40

A high standard deviation suggests variability in responses to the independent variable, while a low standard deviation indicates consistent effects.

Question 41

What is the impact of outliers on the mean and median?

Answer 41

Outliers significantly affect the mean but have little to no effect on the median, making the median more robust for datasets with extreme values.