descriptive statistics

Question 1

measures of central tendency

Answer 1

mean,median,mode

Question 2

measures of dispersion

Answer 2

range, standard deviation

Question 3

measures of central tendency

Answer 3

Measures of Central Tendency: A single value that summarises a set of data by identifying the typical value of the data set, also known as an average.

Mode: The most frequent score in a quantitative data set. If there are two modes, the data is bi-modal, and if there are more than two modes, the data set is multimodal.

pros/The mode is not distorted by extreme scores called outliers
-The mode is helpful for discrete numbers; for example, it can make more sense to say the average family has two children than 1.89 children.
-Giving the modal group is the only way of giving the average of data in
categories(e.g. average pet choice)

cons/X There can be no modes if every value is different or multiple modes; this is EV
especially likely in small data sets. This means in some cases, the mode does
not give an exact average value.
X The mode does not include all of the values in its calculation, so it is not as
sensitive as the mean measure of central tendency.

Question 4

median

Answer 4

Median: The value in the central position of a data set.
The median is calculated by ordering the values from lowest to highest and selecting the value in the middle.
If there are an even number of data points, then the median is the halfway point between the two centre values.

Pros/
-As the median is the central value, its calculation is not affected by extreme outlier scores.
-The median is very easy to calculate.

cons/X The median score does not include all of the values in its calculation, so it is not as sensitive as the mean measure of central tendency.
X If there are an even number of data pojnts, unlike the mode, the “typical” value will be a number that is not one of the recorded values.

Question 5

mean

Answer 5

Mean: The arithmetic/ mathematical average, calculated by adding all the values and then dividing by the number of values.

EV +
Pros/All raw data points are used (represented) in calculating the mean. This means
the mean is the most sensitive measure of central tendency

X Due to the sensitivity of the mean, the mean is distorted by extremely high or
low values (outliers)

Question 6

measures of dispersion

Answer 6

The range: The range is the difference between a data set’s highest and lowest values.
To calculate the range subtract the smallest value in the data set from the largest (Adding one to this figure is also a correct way of stating the range.)

Pro/The range is easy to calculate, especially compared to the alternative measure of dispersion, the standard deviation.

Con/X Extreme scores easily distort the value
X The range does not show if the scores are clustered around the mean
or more evenly spread out.

Question 7

standard deviation

Answer 7

The standard deviation: The standard deviation (SD) is a complex calculation using all data points that produces a single value. The smaller the standard deviation more clustered (less spread out/variable) the values are around the mean.

pros/
-The SD includes all values in its calculation, making it more sensitive than the range.
- The SD provides information about the spread of scores.

cons/
X Extreme scores also distort the SD
X The SD is significantly more difficult to calculate than the range.