8: Descriptive Statistics

Question 1

What does the mode mean?

Answer 1

Value that occurs most frequently in a set of data

Question 2

What does the median mean?

Answer 2

The number in the middle when the numbers in a set of data are arranged in order of size. If the number of numbers in a data set is even, then the median is the mean of the two middle numbers.

Question 3

What does the mean mean?

Answer 3

The sum of the numbers divided by the number of numbers in a set of data.

Question 4

What does the range mean?

Answer 4

The range is the difference between the largest and smallest values.

Largest - lowest = range

Question 5

What does standard deviation show?

Answer 5

A quantity expressing how much the members of a group differ from the mean value of the group. The squre root of the variance and has the same units as the data

Question 6

What does variance mean?

Answer 6

The variance combines all the values in a data set to produce a measure of spread. It is the arithmetic mean of the squared differences between each value and the mean value.

Question 7

How does a grouped frequency table and a histogram look like?

Answer 7

Grouped frequency table have three columns:

1. e.g. age 10 < 25 ….
2. Tally
3. Frequency

Histogram have no gaps between; like a staple diagram

Question 8

What is meant by quartiles?

Answer 8

Quartiles separate the original set of data into four equal parts. Each part contain 25% of the data.

Question 9

What is meant by first quartile?

Answer 9

• The first quartile is the value one-quarter of the way into the data.
• One quarter of the data lies below the first quartile and three-fourths lies above.
• It is also called the 25th percentile and often have the symbol Q₁.
• Q₁ = 1/4 (n + 1)th value

Question 10

What is meant by second quartile?

Answer 10

• The second quartile is another name for the median of the entire set of data and is also called the 50th percentile. Q₂

Question 11

What is meant by third quartile?

Answer 11

• The third quartile is three-quarters of the way in.
• Three-fourths of the data lies below the third quartile and one-fourth lies above.
• It is also called the 75th percentile and has the symbol Q₃.
• Q₃ = 3/4 (n + 1)

Question 12

What is the interquartile range (IQR)?

Answer 12

The range between Q₃ and Q₁

IQR = Q₃ - Q₁

Question 13

Wha is the cumulative frequency?

Answer 13

• To calculate the cumulative frequency add up the frequencies of the data values as you go along.
• This will be represented in a graph, so you can see the median, Q₁ and Q₂.

Question 14

What is meant by variance?

Answer 14

The variance combines all the values in a data set to produce a measure of spread. It is the arithmetic mean of the squared differences between each value and the mean value.

Question 15

How do you find and what does standard deviation mean?

Answer 15

• The standard deviation is the square root of the variance and has the same units as the data.
• (Learn formula)
• High s.d indicated that the data is spread out over a large range of values and vice versa.
• Standard deviation is never negtative
• If all values of a data set are the same, the s.d = 0 since all values are equal to the mean.

Question 16

How do you calculate the standard deviation from a table?

Answer 16

1. Calculate the mean
2. Subtract the mean from each observation
3. Square each of the results
4. Add these squared results together
5. Divide this total by the number of observations (this will be equal to the variance)
6. Take the variance divided by the total number of frequency and square it (this will be equal to the standard deviation)

Question 17

How does a boxer and whisker-plot look like?

Answer 17