Descriptive Statistics

Question 1

What are the measures of central tendency?

Answer 1

• Mean
• Mode
• Median

Question 2

What are the advantages of the mean as a central tendency?

Answer 2

• Very sensitive stat because it takes accounts of the exact distance between all the values of all the data.
• It is representative of all the data.

Question 3

What are the weaknesses of the mean as the central tendency?

Answer 3

• If one of the values is very high/low (anomalies) then the overall mean can be very distorted and therefore misrepresent the data.
• It cannot be used with nominal data.

Question 4

What is the mode?

Answer 4

• The value that is the most common data item.
• If 2 categories or data items have the same frequency the data has 2 modes, I.e. are bi-modal.

Question 5

What are the strengths of the mode as the central tendency?

Answer 5

• Unaffected by extreme values and is useful for discrete data.
• The only method which can be used for nominal data.

Question 6

What are the weaknesses of the mode?

Answer 6

• Sometimes there are so many modes that the data cannot be described using this stat.

Question 7

What is the median?

Answer 7

• Middle value is an ordered list, all data items arranged in order and central value is the median.
• If there is an even number of data there will be 2 central items.
• Add the items together and divide by 2.

Question 8

What are the advantages of the median as a measure of central tendency?

Answer 8

• not affected by extreme scores so can be useful under such circumstances.
  -> unaffected by anomalous values.
• easy to calculate.

Question 9

What are the weaknesses of the median as a central tendency?

Answer 9

• Less ‘sensitive’ than the mean because exact values not reflected in the median.

Question 10

What is the range (measure of dispersion)?

Answer 10

• Arithmetic distance between top and bottom values in set of data.
• calculated by taking away smallest data value from largest data value.

Question 11

What are the strengths and weaknesses of range (measure of dispersion)

Answer 11

Strength:
- Easy to calculate

Weakness:
- Effected by extreme values
- Fails to take account distribution of numbers, e.g. doesn’t indicate whether most numbers are closely grouped around mean or spread out evenly.

Question 12

What is standard deviation (measures of dispersion)?

Answer 12

• More precise way of measuring dispersing of data -> avg distance between each data item above and below mean.
• Smaller deviation, closer together values in set are, larger standard deviation indicates values more spread out from the mean.

Question 13

What are the advantages and weaknesses of standard deviation (measures of dispersion)?

Answer 13

Strength:
- Precise measure of dispersion because it takes into account all the values.

Weaknesses:
- May hide some of the characteristics of the date set (e.g. extreme values).